No auDA don't care about that. The TM can be completely irrelevant to the domain, just as the ABN can be. It's really used just as an 'anchorer' - an official connection to the ultimate entity holding the domain.
What you do have to be a little careful about is eligibility policy. You need to state a 'close and substantial connection' to the name. However monetisation (parking it) is considered a close enough connection for example.
Thanks.....