hell and heaven no.
your psu can run the 2gtx 770 sli perfectly as long as you don't have a i7 4960x oced at max of heaven, 32gb ram and 6 hard disks and power eating sound card etc.
a gtx 770 will draw at max 230w and given that in sli both cards will never reach 100% power draw any 750w psu 80+ can run 2 of them.
There are lotsa 700w running 2x gtx 770 in sli without a sweat and not overheating or reducing lifespan.
answer is yes.
"GeForce GTX 770 2x SLI - On your average system the cards require you to have a 700~800 Watt power supply unit."