Will my Trial progress be lost if I portal to town to sell my junk?

If it's the honour one, you can, on the room selection thing, click something in the corner to take the invitation and continue later, if I'm not wrong

Not sure about portal but when you're viewing the map there's an icon down the left I believe, mentioning "Pause the trial and come back later" or something like that.

Yea you can. But if you portal to town. You can’t portal back to the trial. You need to travel back to the place where the trial starts and the stand thingy will let you continue where you left

They have a chest in the last room where you can store your junk and then sell it once you get to town.