There is an issue with putting anything between a Hollowtech bottom bracket cup and the frame.
A cartridge bottom bracket is not very sensitive to its position being changed relative to the frame shell a little by the chain case mounting bracket. The axle just gets moved slightly towards the drive side.
The hollowtech cups are more sensitive to their position being changed, as they need to be the correct distance apart to match the length of the axle on the crank. If you put something between the cup and frame the cups may be spaces too far apart and you will not be able to fit the non-drive side crank.
However, mountain bike cranks are typically made for 73mm frame shells and MTB bottom brackets are installed on 68mm shells with two 2.5mm spacers. You may find you can omit the drive side spacer to make room for the chain case mounting bracket.
If the bracket it less that 2.5mm in thickness you may need to find thinner spacers to make up the difference and get the correct cup spacing.