I've done it; both are true and yet not the end of the world:

Disconnect the service: this is obvious, but if you're doing this because the service is not usable and you are switching to another provider anyway, so good riddance? Best case scenario they magically fix the problem, worst-case no change.

Collections: yes, they called, I provided evidence of my communication with the provider trying to resolve it in good faith. Never heard back since and it's been 6 years.

Collections agencies have a business to run and focus on collecting valid debt. Invalid debt is a liability to them and they're not in the business of adjudicating disputes, so once provided with the evidence they drop the matter (of course the provider can still pursue you directly, which is why it's important to keep evidence of your good-faith efforts to resolve the matter).