Could Stack Overflow run on SQL Server Web Edition?
Considering that SO is one of the most highly visited sites in the world, it may not be the best site to compare against for a new venture.

That being said, SO, to my knowledge, has rolled their own solution in terms of scaling various aspects of the system, including caching just about everything that they can to remove as much load off of the database as possible. Most systems of the SO scale end up in this scenario because no off-the-shelf product or built-in scaleability feature fully meets the needs of these extremely-high-traffic sites.

So, while I wouldn't be very surprised if SQL Web couldn't handle high traffic loads, I would bet that the built-in scaleability pieces you get from other tiers of SQL Server will not, on their own, be enough to handle these sorts of extremely high loads. (hence why SO doesn't rely on them as their primary scale vector.)

Lastly, the business plan for any new venture that is concerned with a high potential to scale needs to also include a revenue stream that scales along with the business volume (whatever that may be).

So, if you scale in the volume of data your system has to hold and manage, does revenue scale with it? Likewise for number of users, or any other metric that will grow. If you find that you are not scaling your revenue as fast as the expense of scaling the combined metrics, you have issues to worry about.