It should be possible to find out the power drain of a DAB radio by looking at the manual to see what wattage the power supply is, or on a sticker on the back of the unit, Id imagine displaying that somewhere could be a requirement for a CE stamp.
My non-digital clock radio is 5 watts, which is feeble, for a comparison my quite powerful office PC drains 400+.
Interesting snippet on the problem
at this page, where police are complaining that due to a larger power drain on digital radio's the batteries dont last a full 16 hour shift, only managing about half that.