I can only assume you are joking about using a DC ohmmeter on the core of a small signal audio transformer. Doing so would of course magnetize the core and screw up the performance. As these kinds of units use very thin wire, they cannot then be demagnetized as they cannot hold the current that would be required.
It may depend on the meter used for measuring. My Simpson 260 meter would certainly magnetize the core. Newer digital meters not as much.