I suspect that a floating object increase the range over which you have to search. If you object sinks to the bottom, at least you know about where it ended up.
Surface shipping already uses something similar, mounting buoyant distress/telemetry beacons which automatically deploy in an emergency (I don't know the exact mechanism, but I'd assume it's triggered by water pressure or something similar).
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.
Aircraft have floating, jettisonable radio beacons (Emergency Locator Transmitters) that transmit on the international guard frequency 121.5MHz (with intentional harmonic distortion that allow reception on the military guard frequency of 243MHz). That frequency is monitored by SARSAT (Search and Rescue Satellite) in North America -- the middle of the South Atlantic may not be monitored, since the automated search notifications would not necessarily reach anyone able to do much about it. Local air control stations will attempt to determine the position, but ultimately it's usually someone with a portable directional receiver that pinpoints the actual source of the signal. (Occasionally a unit will begin transmission due to mishandling or malfunction, and I spent far too much of my time in the air force trying to sort through ejection seat packs and spare ELTs to find an overambitious backup gone wrong.) ELTs are also normally located on any floatation rafts the aircraft may be carrying.
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).
Radio doesn't work underwater. At 20 meters depth, a submarine can receive a 35 byte-per-second message using a long antenna, but it cannot transmit. [ http://en.wikipedia.org/wiki/VLF ]
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.
Or even better, you could have them produce a sonar ping that search and rescue could listen for... which is what they already do. :-) [ http://trueslant.com/milesobrien/ ]
Flight recorders, along with being incredibly durable, are also incredibly heavy. It would be difficult to provide a remotely reliable method of having the device float.
No, no radio beacons. If they are on land, an exhaustive search finds them. For underwater search, they have battery powered "pinger" beacons. That is the cylindrical item in the picture on the Wikipedia page.
The aircraft itself has a radio beacon that self-activates on a crash. Having one on the black box would be redundant and very likely ineffective since the black box is buried in the guts of the aircraft (e.g. if it separates enough to have a clear field of view for transmitting, it is probably going to be too damaged to transmit).
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).
