That old power supply? I'd get it replaced if I were you. The components in it are likely old, and definitely 100% don't support the 750w's it originally used to.
As long as the motherboard has a PCI X16 slot, yes. It can fully handle a GT 710 GPU, but why are you getting a GT 710? A much better deal would be the GTX 750Ti for like $50 off of Ebay right now.