Dehumidifier to condensate pump?

I recently put a portable dehumidifer in my basement. The humidity is regularly 70%. During this Michigan summer it is filling up most days in an attempt to get under 50%.

I want to use the continuous hose fitting instead of emptying the bucket each day. The utility sink isn't close enough to an outlet without an extension. It seems like I should be able to connect the portable dehumidifier to my condensate pump.

It has four inlets, two of which are occupied by the furnace/air conditioning unit.

I've left it running for a few hours and seems to be working just fine, but not sure if I'm setting myself up for trouble. Is the main concern that I may burn out the motor quicker? If the dehumidifier is filling up each day I would expect the condensate pump to be running a lot more.

To summarize:

Can I safely connect the dehumidifier to my air conditioner's condensate pump?

What sort of connection should I make to the condensate pump? The inlet doesn't look threaded, but the air conditioning has PVC pipes with fittings connected to the inlets. I can't see how that connection is made.

Thanks