Will a Deore M5100 11sp mech work with a 12sp shifter?

I think so. I have the opposite. 6100 mech with 5100 shifter and cassette. Only difference between 5100 and 6100 mechs may be jockey wheels designed to work better with HG+ cassette on 6100?

Try it and see. I expect it will be fine

Edit- this video says they are identical

I have a Shimano Deore M5100 (11 speed) derailleur, and a Deore M6100 (12 speed) shifter and cassette – will they work together?

Are the M5100 and M6100 derailleurs basically the same?

Yes it will work perfectly. I use the 5100 rear mech with slx 7100 shifter.

Excellent, thank you.

Yes, it will work. But it MIGHT not go onto the 10t small cog. They are designed for 11+ teeth wheras the 6100 is designed for the 10t. I was running my 5100 mech with 8100 12sp shifter and 12sp Sunrace 11-51 (or 52 ??)cassette.

The 5100 and 6100 derailleurs are not identical. The 5100 weighs significantly more. Maybe just a heavier metal/plastic, I'm not sure. But they are different.

I ran the other way round with zero problems

6100 mech with 11 shifter on 11-51t sunrace 11spd

so I don't see why not.