Well it depends on who's handling it. If someone like Gene Roddenberry, it'd be another vehicle to look at the weird human condition through the eyes of the Doctor. He kinda tried to make something like that with his "Assignment: Earth" proposal. Gary Seven had many similarities with the Doctor.
Though I'm not entirely sure it'd last as long as Who did in the UK, if it'd even get greenlit. From what I've been told by my British colleagues, the original intent of the Doctor Who series was as an educational device or something. Even then, Roddenberry had a hard time selling Star Trek to the TV execs, becaue at that time the airwaves were largely dominated by Westerns. So the idea of a magical alien running around in a time-travelling box would've been an even harder sell. Hell, Roddenberry couldn't even get his "Assignment Earth" concept off the ground, so it'd take some serious tweaking history-wise to get a world where Doctor Who got made in the US.
Speaking of which... had this crazy idea a few years back... to take a buncha clips from "Assignment: Earth" and a whole slew of b-movies and make a fake trailer/ad for an American Doctor Who series that never was. Had a blast trying to think up movies that had creatures similar to the ones the Doctor faced.