The ulnar collateral ligament of the first MCP joint can be evaluated by MRI, but like most things in life, some do it better than others. A high-field scanner (at least 1.0 Tesla) with strong gradients is critical. With good hardware and proper protocols, one can get excellent images.
The critical question in the setting of a tear of the UCL is whether there is a Stener lesion. This occurs when the torn UCL retracts and becomes superficial to the aponeurosis of the adductor pollicis. The ligament can no longer heal, and chronic instability results. A Stener lesion can be repaired surgically.
Example of a torn UCL, without a Stener lesion:
Thus, in this case, the torn UCL is beneath the adductor aponeurosis, and there is clearly no Stener lesion.
MRI sometimes gets a bad rap for the evaluation of Stener lesions, because the test is often done poorly, and interpreted incorrectly. In the hands of a good MSK radiologist, however, it an excellent test.