No.
Wings create drag of course. Drag is the sum of three different drags, induced, profile and shear drag.
(For what matters here, race cars).
The only one that will increase with bigger wings is the shear drag, which far from being the main component of drag at speeds of race cars.
The induced will depend on the Cl/finess ratio of the wing, while the profile will depend on...the profile.
Thus, and like for every physical system out there in the universe, the efficiency of a system will always depend on number*speed*Geometry that is size of the wing*speed*design of the wing.
IF F1 was using ultra optimized wings, that is with high design efficiency, then yes increasing the downforce would increase drag (not linearly though) but F1 is far from being an efficient aeros formula.
The same applies to engines and tyres. If you seriously think that current tyres are at the top of the technology you're missing something.
F1 is heavily regulated and thus has created technical solutions that are only viable inside themselves.
Again, if you tell any engine designer of the automotive industry and say him "in 3 years i'll have 50% the fuel consumption with the same power" he will laugh out because in automotive industry, for the usage done, the cars are quite optimized (yes okay..a low cost sedan is not..) so technological progresses are hard to materialize, but in F1..this is not too hard because the technologies are there already.