" Do you think my GPU will bottleneck the CPU if I upgrade to a 5800x? "
Most gaming is limited by varying degrees by both the GPU and/or by the CPU...
Certainly the delivered gaming framerates with a 5800X could be higher with a better GPU, but, by that unrealistic 'bottlenecking' cutoff , technically everyone short of a 3080Ti or above is technically 'bottlenecking their CPU', so perhaps better terminology is required. (Like deciding if a system is overly 'lopsided'... and given today's GPU climate, you might very well find a 1070 'sufficient' for 2 or more years. Certainly, no one is likely to claim you 'don't have enough processor' for a decent handful of years with a 5800X, a fairly top tier CPU even after considering Intel's 12th gen.)