Let's cover some Magic fundamentals. It's well known that draft decks are, almost always, better than draft decks. I'm going to talk a bit about why here, and then apply those lessons to figure out how much adding packs to a sealed pool is going to improve the quality of the deck you can build - this is particularly important given the new "friendly" sealed leagues starting now on Magic Online. Let's jump in.
In Sealed Deck (for several years now), you get six packs of product. The big difference is that in draft, you're selecting cards that are best for your deck and passing around, while in Sealed, you are stuck with those cards you open. So in one sense, in a normal Booster Draft, you get to see 252 cards, whereas in Sealed, you are seeing only 84. Does this mean draft decks are 3 times better than sealed? No, of course not - even with selection, and seeing all those cards, you still end up with only 42 of them - half as much as in a Sealed Deck. Moreover, the other players are going to be taking a lot of the good ones, so it's not like you're getting all the best set of cards from a draft pool.
So how much better are draft decks than sealed? Well it's a little hard to quantify exactly, but the method I like to use to get in the ballpark starts with the color pie. In most formats, you want to stick to playing two colors of spells (this goes back to how you build mana bases - 3 colors are very hard to pull off without lots of fixing, and the math simply dictates your consistency is too low most of the time). What this means is that you're only playing about 40% of your colored spells in a typical Sealed format. In draft on the other hand, you get to draft to your two colors, by-and-large. You rarely actually get to the best case of all of your picks being in those colors (at the end of packs, you're stuck with whatever is left, and early in the draft, you may end up jumping around a bit before figuring out what your colors actually are). Still, this best-case-scenario gives us some rough guideline, which we can adjust later.
If we assume that everyone in the draft is on 2 colors, then that works out to 16 color-drafters, or about 3.2 drafters per color. This leads us to getting about 31.25% of the cards in each of our colors. We can easily round this down to 30% as a nice ballpark number (and because of the reasons listed above about jumping around colors, as well as splashing against us). You're also getting 12.5% of the colorless cards (generally artifacts and lands) as opposed to the 100% in Sealed (so this is one place Sealed has the edge).
Now you have to add in that you generally play 23 spells, and the rest of your deck is generally basic lands (obviously, some formats are exceptions to this). Maybe you add in a couple sideboard cards to the count - it doesn't make a massive difference. How much of the format is that? I'm going to use SOI numbers here, as it seems fairly typical - your mileage will vary a bit, but again, we are just ballparking here. Roughly 8.5% of the set are the colorless cards, which leaves about 18.3% for each individual color. So in a draft, you're getting about 30% of two of those colors, and 12.5% of the colorless.
23 out of 42 cards gets you to 55%. One of those cards is, on average, a land, and a couple more or probably in other colors, which means the real percentage of cards in your colors is going to be closer to 60%, or even a bit higher. 60% of 30% is 18%. So you're looking at getting about 18% of your colors' cards in a draft., and about 7% of the lands and artifacts.
Of course, this is a lot of assumptions - both the 60% and the 30% are going to be a little high, I think, but only by a couple percentage points - so maybe you're really looking at 17%. And beyond that, you get to take into account that you're making a deck - which means that archetype considerations might come in, and mana curve considerations definitely will. But again, this is a ballpark number. If we multiply this out by our 3.2 drafters, this means that we're peeling off the top 55-60% of cards in every color, and it's more or less only those cards which are making their way into draft decks.
In sealed, we still usually play 23 cards, but now we have to pull them from from 2 colors of the pool. So we have that 18.3% of cards in a color twice, plus 100% of the colorless buddies. This works out to around 37.9 cards, rather than 42 in a draft. If we exclude lands, we get to 35.5 cards instead of 40.8. 23 divided by 37.9 gets us to pulling from the top 65%, which means we have to dig about 10% lower than we did on the draft side.
Now, there are of course a lot more differences - on the plus side for draft, we noted that we can play more to archetypal synergies, and have a better curve. On the sealed side, colors are probably not split 100% exactly 5 ways, and this is especially going to be more true of bombs (higher rarities -> fewer cards -> variance is more of a factor, and you still get to choose).
So we can expect draft to be a higher margin better than sealed the more two-colorness matters, the less high-rarity cards matter (i.e. the flatter the power level between cards), and the less good colorless cards (artifacts and lands) are.
Okay, great, Sealed is very roughly 10% worse than draft, I have no idea what that means for win-rate, and there are a whole bunch of caveats. What did I mean when I was talking about the Friendly Sealed then?
Well, you get the option to add in a 7th and later an 8th pack. How much of a difference does that make? Well, it's 1/6th better, then an additional 1/7th better, which works out to 1/3 better by the end? But in more relate-able terms, using the methodology described above, which takes into account the realities of color limits, 7 pack sealed is slightly stronger than draft on average (much closer to draft than 6 pack sealed), and 8 pack sealed is a good bit stronger still (roughly as much better than Draft than Draft is to normal 6-pack sealed). This is without taking into lands, which mostly means extra fixing, which means splashing and/or 3 colors is more likely with more packs, which means... well something, but I assume that the extra pack sealeds are even stronger.
Long story short, adding packs makes a big difference in deck quality, and I would expect you to not be able to compete very well without doing so (when faced against people who are).