So the answer is a qualified yes.
If it's an EAB, the examiner will have to agree to fly in it.
It has to have the instruments needed to demonstrate the 'fly solely by instruments' tasks on the PTS.
It has to have dual controls.
Your wife will need to be a named insured on your insurance. A cfi will probably want to be named too.
Bill is correct. This is not a FAA requirement, but is a practical consideration for most people. (Many new people are unaware of the tight restrictions on typical aircraft policies, compared to cars.) Same is true for the instructor. Some instructors with little assets will not care if they're covered or not.