Sure, you can use them. Just remember their range is generally much less; of the order of 10-20nm. Having said that, yesterday I was picking up Shoreham from ~50nm and that is common.
To be picky, the airport DME will be set up to read zero when you are at a certain place (not necessarily at the centre of the runway) and this can cause small errors (a fraction of a mile) if you are in an altogether different direction. I don't know of any cases where you would get huge errors.
Most of the time, a DME is within a fraction of a mile of the GPS distance, and that's plenty good enough for backup purposes.