I converted my triple to a double by only changing the crankset and BB and it works for me. I can't speak to whether a true double front der would be much better, I still have the triple on there. It would make sense to me that the double derailleur could perform slightly better as it doesn't need as long of a cage for the capacity.

The most difficult part is getting the indexing right after the switch. I believe most recent Shimano groups have a universal front shifter, it's just a matter of setting it so the stops are in the right place for a double. In my experience, the double doesn't actually shift any better, it's just that there is less fiddling needed to get the indexing correct, and you can use a wider range of rear cogs for on a given chainring resulting in less shifting.

I say go for it, if it doesn't work well enough for your taste you can change more parts as needed. If it does work, you have a very easy switch back to a triple in case you need it for a particular ride.

EDIT: Just noticed from the post above that you're talking about a compact. I changed to a standard; I haven't ridden or set up a compact so I don't know if my advice still holds.