Any processor not maxing out/saturating a GPU is technically 'bottlenecking' it somewhat, but, the issue is to what degree, and, of course what resolution you play with. If you were satisfied with framerates before your GPU died, then the processor will at least equal that framerate after getting a faster GPU...
Much also depends on the game, some are already down a handful of percentage points with any pre-8th gen i5, and some run great. (BF1 loves threads, for instance) However, even if you do not get the absolute max the 1070 is capable of at 1080P, it should be faster than what you had (if less than a 1070), and, you can take it with you next CPU/RAM/MB upgrade...(Eample: getting only 80-90 fps with an older i5 instead of 140 fps with latest i7 is hardly 'unplayable')