Road side with a frame pump you might not get too high a PSI. However with my floor pump, I can get way higher than the 125 PSI my air compressor will put out.

I'm of the opinion you aren't going to hurt the tire itself very much with too high a PSI, but you do risk it blowing off your rim if you don't reduce the PSI to within limits. And if it blows off the rim while you are filling the tire, you better hope your hand isn't right there where it blows off. Hurts like heck, and you'll be wondering briefly if you need an ambulance.