Quick search only, found that and it discuss power reqiurements. Your card needs at max 250w so it needs more than just a eight pin. But in theory you can connect only the eight pin and have a go while you wait for the six pin cable to show up. The eight pin can deliver 150w so that should suffice for 80% load or somehing. (power consumption isn’t linear with load)
But not getting enough power can make computing innacurate and cause buggyness and drawing too much from the psu can harm it apparently (if I understood it correctly)
That’s all I can say and I am already in deep water, so good luck and if you feel adventurous then be carefull. Don’t want you to break anything.
Your 650 psu should be strong enough as the 1080 ti has 600w as minimum for system. (but not if you overclock your cpu, has two gpus etc)
6+8 is not unusual by the way, but only used for cards with high power needs. (top performance cards like ti models, oc models and/or those with multiple fans at the same time)
All that said, I recommend connecting both cables. (But being who I am I know I couldn’t resist trying… ) So read up, be smart and Good Luck!
Edit: by the way, using a 6 pin out from the psu with a converter (in your case the 6 to 8 cable) is fine! No worries there.