I read anything stored in there is safe and dosen't disappear but i haven't as yet left anything myself, I assume IG only you and the Alchemist that left the journal had found the shack, and the Alchemist is dead somewhere, I actually headed out and looked for his corpse or proof he existed once for hours lol :/
Didn't find him...
I'm not concerned about thievery, more about the cell reseting and then you losing all your stuff.
If anyone knows for sure, I'd like to know. It's a great place for such a character.
EDIT: Found this on UESP
"
The end table next to the bed doesn't respawn. This makes the Alchemist's Shack a nice place to use as a base.
Testing the resets for the Alchemist's Shack has shown that the outside barrel and the inside barrel do reset and so do the items in the shack, meaning if you move items from their spot or take them they will respawn in their original spot. However, the moved item will not disappear meaning you can duplicate the original items.
Also note that the satchel does respawn. If you put ingredients in there, for example, you will lose them after a period of time."
Might actually use the place and then perhaps eventually move to Riften (feels like a more hunter/alchemist house with a door that goes also directly outside) with a character build like this.