Sending a signal makes it easier to find - that's not stupid whether or not it sinks.
Sinking means that it doesn't move much. However, since it's attached to the plane, it's likely to go down with the airplane whether or it it would sink on its own, whether or not it sinks on its own is irrelevant.
The aircraft itself will also carry an underwater acoustic beacon (pinging at about 40KHz) or two so that underwater wreckage can be located once the general area has been established by the ELT that should have been jettisoned on impact. Both items (the ELT and the UAB) have limited battery life -- they pump out huge signals relative to their size. By convention, the UAB is located in the same general area as the FDR and CVR longitudinally.
In the case of the Air France flight incident, it would seem that the ELT did not work or was at a significant distance from the crash site by the time the search reached the position. That the black boxes (the FDR and CVR) are expected to be recoverable at this point seems to indicate that the UAB did work (it would have been detected by a sonobuoy dropped by the search airplane, which looked to me like it was equipped with anti-submarine warfare equipment, judging by the MAD boom on the tail).
Some modern recorders on board aircraft can apparently do similar tricks, but I'd imagine it's more difficult to make it work reliably; the stresses involved in a plane crash are likely far greater, and I'd suspect the number of places from which a device could both survive and get free to deploy is much smaller.
http://en.wikipedia.org/wiki/Emergency_Position-Indicating_R...
The ELT is to locate the debris field. (OK, it is officially to locate the survivors, but they tend to be in the debris field.) If the crash is on land, another radio to locate the black box is unnecessary. If it is in the water, a radio transmitter is useless, but a pinger is very useful (see other debate threads why floating black boxes aren't a good idea, and impractical to boot - the armor is very heavy).