The BBC time signals are taken from the National Physical Laboratory. At the moment there's no way to allow for the processing delays of DAB but, once the FM transmitters are turned off, it's possible that the BBC could use an adjusted signal so that everyone heard the correct time on DAB. However that would result in the Long Wave and Medium Wave transmissions having a time signal which was slightly too early, so I doubt that any changes would be immediate. (There are currently no plans to switch off the LW & MW transmitters).
Further, Radio 4 still uses Big Ben for some time signals. (No, it's not a recording. There really is a microphone in the tower!). Unless the BBC broke with tradition, and switched to using a recording of the chimes, either Big Ben would have to be set incorrectly or we'd still have a time signal which was too late on DAB!
Chris