If you have been requested to attend an Independent Medical Examination (IME) by your disability insurance company, in most cases, the examiner will not allow the session to be recorded. You can certainly request it and they may permit it. If you refuse to participate in the assessment on the basis that you were not permitted to record the session, the insurance company will probably treat that as non-cooperation and may suspend or terminate your disability benefits on that basis.
As Part of Litigation
When you are in the midst of a lawsuit with your disability insurer, there may be circumstances in which a Defence Medical Examination (DME) can be recorded as a matter of right. This will likely be resisted, even if compelling arguments are made as to why recording is being requested. The question of whether recording will be permitted in these circumstances is something you should discuss with the lawyer handling your claim to discuss your particular circumstances.