There have been a couple times when I don't think my tent got to dry out for a week straight. It got packed into a dry-bag every morning with it wet. I was concerned in the beginning, but the tent never showed a sign of any issue. I don't worry about it anymore. However, I would Not leave a wet tent packed for multiple days. Either use it or dry it out.

Hammock is the way to go!

I tour for two weeks at a time on logging/minining roads in Northern Ontario Canada. Sometimes it rains heavy and long. I've taken to first pitching a light-weight tarp over where my tent will go. That allows me to pitch or take down my tent without the tent getting wet even in a heavy downpour. The tarp is useful for other things too.

Cheers

I've done dozens of two or three month tours primarily camping.
Except for places like Nevada, I just roll it up wet - but - -

My tent is always easy to access -
When the sun comes out, bright and strong,
I pull it out and spread it on the ground.

Even one day cooking in its own juices, a tent gets skanky.
And yes, it gets difficult when you have day after day of rain.