Why would anyone select 7700 and not tell ATC anything?
Yes:
1) Unable to transmit voice (headsets failure, radio failure)
2) Unable to speak - loud cockpit noise such as canopy failure, partial pilot incapacitation, cannot speak audibly due to 3rd party (terrorist situation)
we even have codes following 77xx, to mean other failures, Hydraulics, Electrical, oxy, etc...