Upgrades aren't a benefit at HGI but I have been upgraded if they have the inventor usually.
I stay at the HGI times square north a lot and they charge more for a corner room which I like. I used to always get upgraded in the past and last time I stayed there there was a nor-1 for $9 and also another option for a 2 p.m. checkout that was either $20 or $40.
I didn't select either and requested a corner room in the comment. When I did the online check in corner rooms were showing up with no additional charge and I got a 3:30 p.m. check out with no problem.
I you don't know the room numbering system of the property I would skip the online checkin and just ask for that room type at the property when you arirve.