I think there's a technicality here. Both the operator and the radio station each need, independently, an FCC license. The operator license requirement has been waived for pilots for a long time, and in 1996 the requirement for the plane to have a station license was dropped so long as the airplane is in US airspace. When you operate a handheld in the plane, you are operating a second radio within the same station (the airplane) so you are covered on both counts.
The problem is outside the plane you are not operating in a licensed or license-waived station, so you would need a station license for the radio, AND you'd need a restricted radio-telephone operator's permit because you don't fall under the pilot waiver because you're not flying a plane.
Virtually ANY ATC facility will not know any of this and will almost certainly give you a radio check. It would be a very rare circumstance that anyone would call you out. I wouldn't do it on clearance delivery at O'Hare, but elsewhere it's unlikely anyone will care. Unlikely they'd even ask for a tail number if you said "Rochester Ground, how do you read?"
But as the previous poster points out, it is technically illegal and can have consequences. I have both FCC and FAA licenses and I too have heard of people being convicted for transmitting on public service frequencies. So I'll clarify... If you are a pilot, AND you are at the airport, and you are making a legitimate radio check, it is technically prohibited but you would have some latitude that a layperson would not. But if you are not a licensed pilot to begin with, it's probably not the best idea.