Will this CPU bottleneck this GPU

Yes, it'll bottleneck at stock clocks.
My brother's Phenom II 1090T bottlenecked his GTX 560 severely in DayZ, even though the Phenom II 1090T is stronger than the Athlon 750K and the GTX 560 is weaker than the R9 270.
http://cpuboss.com/cpus/AMD-Phenom-II-X6-Black-1090T-vs-AMD-Athlon-X4-750k

A Pentium G3258 would beat the Athlon 750K by a significant amount, and would not bottleneck an R9 270. It's a much better option.
There's absolutely no reason to buy an Athlon 750K or 760K new anymore, as the Pentium G3258 is faster, cheaper, games better all around, overclocks better, and consumes less power.

Check the forums of DayZ and every single MMO including TESO. Droves of people commenting that their FX-8320s and FX-8350s drop into the 20 fps range regularly on medium settings, despite having strong video cards. Athlons score worse. AMD CPUs are terribly weak for anything AMD doesn't pour money into trying to force their outdated and inefficient architectures.