I have a nest thermostat connected to baseboard hot water and central air. I'm looking to add a C wire to the nest for constant power. Can someone confirm if I should connect blue to to brown from the unit?
Yes, you're correct
Based on both the way your air conditioning compressor is wired and on the wiring diagram for your air handler, the brown wire in the thermostat wiring compartment is indeed the C wire you're after. So, simply incorporate the blue wire into the existing wirenut junction at the air handler end, and you'll have a C wire at your thermostat!