I'm not an HVAC pro or a plumber, just a homeowner, but I'll share the little I know.

The problem with vent stacks is that they exhaust sewage gases (smelly and often flammable) from the house's drain lines. You wouldn't want to connect straight in and code probably doesn't permit doing so because the gas would flow out that connection line.

Assuming your talking about condensate from an AC coil and not from a higher effiency furnace, you want a drain connection to be behind a trap. I don't think putting a trap in the pipe you're proposing between the AC coil and the vent stack would work because it would dry out after cooling season.

A small second home I have in that's in a commercially built housing development has an arrangement under a bathroom sink that looks like this:

I think that would solve your problem and be safe and code compliant.