An update of your gpu will help with better real time playback of clips carrying lumetri effects, it will help with playback of R3D (hopefully much more soon if adobe also integrates the new SDK for Red as Resolve already has) and it can accelerate the neatvideo render a little. In general your export speeds will increase a little as well.
It will not help with decode of the xavc or other gop based codecs (h264) nor with the speed of analyzing footage for stabilization. Those are cpu bound tasks.
You can check the gpu section of pugets premiere pro site here: https://www.pugetsystems.com/recommended/Recommended-Systems-for-Adobe-Premiere-Pro-143/Hardware-Recommendations
While the 1060 is no longer on there, it likely compares to a little under the 1660ti. While upgrading to a 2080ti is better, even a 2070 super will make for a solid increase already. Biggest differences will be export speed (and render speeds of newtvideo) and real time playback of the red files (u can do higher resolutions with the 2080ti). My guess is the effect on the responsiveness of the lumetri panel is likely very comparable.
2080 ti is the card I would buy if I were building a system today and if budget allows it. I think it is the best “value for money” card since it easily competes with cards of 3000$ or more (like titan rtx or quadro).