Even if on separate to let's DL will thru check bags to MU. Same in reverse. On way out you will have to clear Canadian immigration and pickup bags at YYZ, AND RECHECK WITH MU. Thus there's little benefit in thru checking them. Unlike YVR, there's no ability to skip Canadian immigration at YYZ T3 and bags don't transfer.
T1 where AC and UA operate I believe has a setup that allows you to skip entering Canada. However T3 doesn't.