It's adding machine hours to your machine. It would dry it out, but it also increases your leak rate a lot.

What you could do is get an AC powered mattress inflator like this detach your hose from your machine in the morning, hook it up to the inflator while you shower, and it should be dry by the time you get out.

I haven't done this myself since I like a lower moisture level, but it should provide enough airflow to dry out the tube.