I have asked quite some people about that fact…
The ones, who are working at a Mac Service Center say, that the Mac can handle the card I have.
There are actually two type of cards of the 580’s: the GTX580 with 1.5GB and the GTX 580 with 3GB. The 3GB version needs an additional power supply for sure, but not the one I own (1.5GB). I run the card since August 2012 in my Mac Pro 3,1 (early 2008) and it does a good job. The Mac people said, I should have no worries about damaging my Mac Pro.