This depends. If the transmitter you use for analogue reception also transmits DTT signals then you shouldn't have a problem, but if it doesn't, then the nearest transmitter that does could be out of range. Most relay stations are analogue only and some may never be upgraded to digital.
The best thing to do is to borrow a box and see if it works. You should also get a proper indoor aerial instead of using the small loop aerial supplied with the TV, possibly in conjunction with a signal booster. Go to
www.dtg.org.uk and check your coverage.
I'm two miles from the Sudbury transmitter and reception with an indoor aerial is fine on all channels, although the Sky channels do break up a bit if the battery is low on the signal booster.