[papajam]

Welcome 87quad!
Adding a load such as the A/C when the engine is idling will tax any charging system. I would verify system voltage with the A/C both off and on at the battery with a voltmeter at idle and 2000rpm since the accuracy of the dash voltmeter may be in question. If the voltage doesn't go up to at least the low 13v range at 2000rpm, I'd say your mechanic is right. You also might consider taking the car to an auto electrical shop where they can properly loadtest the alternator in situ.