Double taping or double wrapping is definitely common, and as with all things bicycle there are various opinions on the best way to do it.
I do it mostly for comfort, although as with many others I do have hands big enough to comfortably hold the bars when they're bulked up like that (I'm using two layers of foam tape rather than an under-layer of cotton tape).
I'm not sure there's much advantage to using a layer of non-padded tape, but if it works for you go for it. It's easy enough to remove, so at worst you've lost whatever you paid for the tape.
What I usually do is buy bargain-bin tape for the bottom layer because no-one sees it, and I'll often wrap top-down because I think that works better. I don't tuck the first set of tape into the bar at the bottom, only the outer layer starts tucked in. And I'll often run the outer layer a turn further up towards the stem so it's anchored onto the bar rather than just the first layer of tape. I get that extra tape by only wrapping round the brake levers as little as possible (ie, I don't do the extra figure-8 around the levers), partly because the extra padding often spoils the feel of the levers.