SRAM X01 Eagle 12s RD adjustment to work with 11s cassette + shifter?
There are two things that must be correct to move the derailleur  the right distance for each shift.

Cable length pulled per shift
Derailleur actuation ratio - ratio of lateral cage movement to cable length pulled.

The 11 speed shifter will pull the correct amount of cable for the 11 speed cassette sprocket spacing through a matching 11 speed derailleur.  If the 12 speed derailleur has a different actuation ratio the cage will not move the correct distance. There is no adjustment for this.
The X01 Eagle uses what SRAM calls ‘x-actuation’ ratio, GX seems to use x-actuation and ‘exact actuation’ ratios for different components. The Exact actuation ratio is a little different and not compatible.
Check which exact model I’d grip shifters you have on the SRAM site. If they use x-actuation your proposed setup will work. If they use exact-actuation the setup will not work.