I read about a guy on Jalopnik who rode a Grom from Portland to Anchorage, I don't know if that's a greater condemnation of his decision-making skills or a higher endorsement of the Grom's capability. It's a nice little bike, operative word being little. I think it'll get you anywhere eventually, your greatest consideration being that you shouldn't be in a hurry.
RE: potential top speed with 125cc, that's a tough call but this guy:
214 mpg with DIY aerodynamic fairings on a Honda 125cc motorbike got a 125cc PCX to boost from 56mph to nearly 70mph before he even got around to adding slick bodywork or taller gears. All he did was convert it to a feet-forward seating profile for radical frontal area reduction.