I had a similar query recently - 2 people, 2 bikes, 1 kickr snap = erratic resistance
I will say, it has not been smooth at all for me. There may be other variables at work (changed my trainer bike, TR beta app, PM for cadence), but I have tried a number of different approaches and still having major issues - mostly on my side. For me, using TR, Stages and Snap. For her, just the Snap and a cadence sensor. My TR workouts have become much less stable with much higher resistance. This coming from ~4 years of near flawless operation. Still trying to suss out, but frustrating.
Not saying you will have those issues, fingers crossed, but something is awry in my household.