I'd would have no qualms doing this myself.
The NEC would even be happy so long as there aren't 20amp receptacles on the unit. This would theoretically let you plug 20amp devices into the 15amp circuit.
Even so, just don't plug 20amp devices into the surge protector and you'll be fine. But I wouldn't even consider that the biggest danger. Instead, you are far more likely to plug in multiple devices with 15amp plugs, resulting in a draw greater than that of a a single device with a 20 amp plug. Keep in mind that you're not supposed to use 100% of a circuits rated capacity. You'll always want at least 20% head-room.
The internals of the surge protector are almost irrelevant. Even if fused at 20 amps, it is likely a slow burn fuse. Meaning, the breaker will always trip first and the fuse will only blow if the breaker fails completely and doesn't trip when it should. With the breaker rated at only 15amps, it will actually trip sooner, providing better protection. A truly anal safety freak would wire their home with 12 gauge wire but use 15 amp breakers.
In summary, if you have no 20amp devices, there is absolutely no danger whatsoever in running the 20amp surge protector on a 15amp circuit. It is roughly the equivalent of running a plain old power strip.