I've never flown the corridor myself but from what I can find online it looks like a U-turn would be a case of "legal but not safe". 14 CFR 93.350 defines two different types of traffic in the SFRA and the FAA's kneeboard guide has a 'plain English' summary:
- Fly in proper altitude range
- Transient operation* [1,000 ft up to, not including, 1,300 ft MSL]
- Local operation** [Surface up to, not including, 1,000 ft MSL]
It also explains what those operations are (emphasis mine):
Transient operation: Aircraft transiting the Hudson River Exclusion from end to end without intending to signicantly [sic] change heading, altitude, or airspeed.
Local operation: Any aircraft within the Hudson River Exclusion that is conducting an operation other than overflying.
Those definitions certainly seem to allow for turns and maneuvering as part of "local operations". However, as Dave pointed out, the corridor is very narrow and maneuvers in a fixed-wing aircraft might be risky. In fact, there's already been one high-profile accident in the East River corridor where the aircraft hit a building after trying to a make a tight U-turn in a strong wind. I suspect that most aircraft maneuvering actively in the SFRA are probably helicopters rather than fixed-wing airplanes.
If you search newsgroups and forums about this you'll find a lot of comments about helicopter traffic at very low altitudes, and many pilots say that turning in the Hudson River corridor isn't a great idea. This thread is a good example.
The FAA has a safety course for the SFRA, by the way. I haven't done it but it might have more information.