We might need New Judge's expertise here for a definitive answer but admitting to one criminal offence doesn't seem like the basis of a good defence for another one to me. (Failing to notify DVLA of a change of address is a criminal offence under Section 99 of the Road Traffic Act 1988. Maximum penalty = £1000 fine).
However Section 14 of the Magistrates' Courts Act 1980
might be relevant here:
https://www.legislation.gov.uk/ukpga/1980/43/section/14
We don't know though exactly why your friend's licence was lost. i.e. what was she actually charged with? 'Cutting someone up' wouldn't normally result in a driving ban unless, possibly, the 'totting up' rules came into play. That's because it would normally be seen as a momentary lapse ('Driving without due care and attention') rather than the far more serious charge of 'dangerous driving' (which always results in a ban).