Will 20's turn my car into a pig?

[LunaZ]

I know that by going up to a larger diameter, wider wheel, I will be increasing rotational mass and unsprung weight, all around... that's the obvious answer.

The question is, will it turn my car into a poor handling, slow accelerating pig that I won't enjoy driving on my favorite mountain roads?
To be specific, I don't need to worry about how slow my lap times would be at the track with a 20" wheel setup. My 370Z is strictly a road car.
I'm thinking that the 370Z has adequate enough power that I won't feel the weight during acceleration, but I'm wondering how the suspension will do with the extra weight.

I'm considering a set of Venaci Spirits like kevr6 has on his car as well as some of the the other wheels forum members are trying to unload.

Serious input that doesn't debate the merits of Miata doors appreciated.