Probably.
As long as you use the correct adaptor for the size of the rotor you ought to be reet: both callipers are designed to bolt stright onto a post mount fork with no adaptor (except the spacers on juicys which can be taken as a given part of the caliper rather than the adaptor for the purposes of working out your adaptors). So all the adaptor does is convert from IS mount to post mount and add a certain distance (in this case 12.5mm) from the wheel axle.
In practice avid adaptors seem to have the post mount holes drilled ever so slightly further over to the left ( I use juicys on shimano mounts on one bike with a timy bit of filing on the conical washers which sit too far out of the right side of the adaptor)) and this could mean aligning the calliper becomes a bit of a mission if it doesn’t slide far enough to the right to sit central over the disc rotor. You won’t know until you try as it will be a matter of 1mm max. If that happens you could either space out the adaptor on the fork/frame mount, or space the rotor out on the hub mount.
EDIT: oh and a) like most other disc brake manufacturers, shimano don’t honour garauntees if you mix and match parts from other suppliers
b) you can’t get 185mm adaptors made by shimano cos they don’t make 185mm rotors either.
But it will most likely be fine.