Laundry sink can be used for condensate discharge; the only restriction in case it has an overflow installed is that the condensate drain tubing must terminate at least 2” above its rim / edge. If there’s no overflow hole (I can’t see that on your picture) – 2” above the sink’s edge. So, this particular requirement hasn’t been met and the pipe doesn’t look supported / secured at all, there’s no trap on the line as well.
Your local municipality might require two condensate discharge pipes in some or all locations, they might also permit single pipe with additional protection devices in place, such as safety switches that turn off the system in case of a clogged discharge pipe. Maybe one of those devices has been installed inside the coil compartment (and it’s not visible).
It might be also difficult to convince anybody that the condensate liquid was responsible for clogging of the laundry sink; it’s just slightly acidic water with dust particles. I’d start from the building department to make sure what’s required in your area and after that verify your installation.
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