I don't know if it would - but there shouldn't be a need to get it on the frame anyway - if the trigger group gets really dirty - get some Gunscrubber at Wal-Mart - there is a synthetic frame version (basically, for polymer frames).
But, with the slide off of the frame, there should be no need to get hoppes on the frame anyway.
It probably wouldn't do anything - but FN puts in their manual not to use lubricants with teflon in them. Evereyone is a bit paranoid about this. Because of that - I'd try not to get it on the frame.
I rarely use solvents - as I use Breakfree CLP for oil and cleaning. One out of every 10 trips, I get some fouling on the outside of my slide (a hard chromed slide). Whenever that happens - I have to use a tiny bit of hoppes put on a cleaning patch. If I wipe it across the "spot" a few times - the fouling always goes away.
Realize - while some guys might be bale to do it - as you shoot the gun, there will be some "crud" and black marks that appear over time around the slide area where the firing pin section is (where the back of the csings hit the slide). Getting the gun as clean as it was when it was new and unfired isn't really practical. Silver slides show more of the grime than guns with black slides. Just clean it reasonably. The Hoppes should do it for U.