No.
A psu will only consume the wattage that is needed at the time, regardless of it's top power capability.
A cheap psu can damage a motherboard if it has a bad design and/or becomes defective. A quality psu will never damage components.
A psu is the last place you should economize on a build.
My short list of quality psu's would include Corsair, PC P&C, Seasonic, XFX, and Antec. There are other good ones, but you can't go wrong with any of those 5.
Here is one list of psu's ordered by quality tiers. It is a work in progress, but it will give you some idea of where other psu's stand.
I don't see gigabyte on it.
http://www.xtremesystems.org/forums/showthread.php?108088-Official-XS-Power-Supply-Ranking-Phase-I