Wilkinson tells us they 'passed as man and wife'. Passed, not lived, which suggests to me they they may well have presented themselves as Mr and Mrs Kelly in a situation where it was unlikely that anyone would contradict them - when they were hopping for instance. That is certainly speculation, but is hardly 'wild'. It's what unmarried cohabiting couples often did at the time.
It seems Kate may well have pretended to be Conway's wife. And why would that have been? An attempt to cling to a shred of respectability I'd imagine. The same reason she might have for passing herself off as Mrs Kelly.
I'm not sure if you've seen the list of names used by/attributed to Alice McKenzie:
I've cheated by adding McCormack because I've never seen that name used for her in print, but I'm pretty sure that there will have been people who knew her only as Alice, the 'wife' of John McCormack.
This may also be of interest. It's from the habitual criminals register (can't remember the date off the top of my head) and it shows how common the use of the name 'Kelly' was as an alias: