Can I leave a wall primed, but without paint, for several sunny months?
It depends on the primer. PPG has over 100 different types of primers.
https://www.ppgpaints.com/search?term=primer
Edit: Since you referenced KILZ 2 primer, and I’ve been asked to direct comments on it specifically, I’ll elaborate: 1) KILZ 2 primer comes in various types: interior/ exterior, mold resistant, etc. Depending on the exact type, some perform better than others, 2) KILZ 2 primer is a latex primer. Latex primers have a shelf life and limited performance, 3) Some primers have a UV resistance, this primer does not stipulate that criteria,
However, leaving wood siding and trim exposed to the weather is dangerous and may cause the material to be replaced.
Summary: If the primer goes “bad” and needs to be touched up in a year or so, it’s still better than leaving wood untreated and exposed to the weather.