No it does not work like that. Like I said there are disadvantages to a VAWT, but do to larger surface area (without having to massively increase the size) it pretty much makes up for it. There are things to take into advantage when comparing surface area though. On a HAWT the blades are always providing thrust under wind, but a VAWT might provide thrust on say between 1/4 and 1/2 of the rotation and part of the rotation on a single blade is drag. Also some have better high wind performance and some better low wind as there are many types of VAWT (pretty much one type of HAWT).
There are drag and lift type wind turbines and even these come on very different types, from Lenz, Darrieus, Giromill, Cycloturbine, and Savonius. On top of that the blades can be twisted (Helical) on most of these types to decrease thrust pulsing. You can also combine a thrust and lift type together. For HAWT you have number of blades, upwind or downwind, TSR, and type of furrowing. Most of these are also done on VAWT (and more)... like variable pitch, number of blades, mechanical breaking, height to width rations, blade thickness...
Say you take a Savonius type. and Helix it like that HelixWind turbine. The surface profile (not counting the twisted surface) you are looking at a massive wind profile of 4'x8.5' or 34 square feet, but do to the limited arc that the air pushes on and the drag you are actually having about 25% of that are as being productive at any one time, so say 8.5 square feet. Now take a 12' HAWT and the 3 blades are say 9" wide (5 feet of blade plus the hub) then you have a nice 11.5 square feet of blade surface area producing thrust. This is very vague but gives you a rough idea. The big thing is that the HAWT does cover a much larger area, the blades spin much faster at the tips, and there are much more thing to mechanically go wrong. It is just weaker. . It is just larger, noisier, and harder to maintain, but likely easier to build.
Now it is not strait forward like this and there are Soooooooo many variables to effect this. Simple blade geometry, balance, and how well the turbine fits to the generator along with tower height and wind conditions and blade material... The whole thing is coming up with a combination of everything that works the best. Hughs has a good design and many people copy that. VAWT are a bit different and unless you want to just make a basic Lenz or Savonius, then there are a lot of things you need to figure out. There is just not too much information out there on how to make a VAWT. This is the biggest advantage of HAWT. There are tons of web sites and book on how to make a HAWT. I think with a good design and the right materials you could make a VAWT as efficient as a HAWT and likely have it tougher.... but it would require a lot of work. I think some are getting closer.