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Does it work?
Given the state of my mech I'm in the market for a new one.

12 speed is ok, but my understanding is that for 11sp that the pull ratio is different enough for them not to work
Different pull ratios, you won't line up all 11 clicks.
I'm using an 11speed (Gripshift) with an M5100 mech, but that's on a 10 speed cassette,.
SRAM 11 speed "X-Actuation" is close enough to Dynasis 10 speed click for click that it works with one dead position.
They work. I've run most combos of SRAM/Shimano 11sp and it works fine. I can't tell any difference in shift quality. The official answer though is no, since the shifters pull slightly different amounts of cable (about 0.1mm different).
Shimano XT vs SRAM GX mechs is a no-brainer IMO. Low end SRAM derailleurs are such trash and I can't bring myself to pay the ridiculous prices for their high-end ones.
The Shiftmate compatibility charts suggest it should work fine. If it didn't they'd sell you a Shiftmate to make it work.
http://www.jtekengineering.com/shiftmate/shiftmate-compatibility-charts-choices/
I run a SRAM X0 11sp shifter, with an XT 11 speed medium cage mech and SRAM XG1150 cassette, it shifts perfectly.
Works great - 11 speed GX shifter with a XT mech here.
I'm now running an X1 shifter with XT mech a Sunrace 11-46 cassette and a 12-speed SLX(?) chain.
I think it's shifting better than it ever did with SRAM derailleurs.