As I'm fond of saying... it's stainless, not stainproof!
Typically an un-passivated surface only incurs cosmetic corrosion -- staining, and does not accumulate rust as such. Or if it does, the rate is extremely low.
Rust staining is still a rough and porous deposit, so it can trap bacteria and hence passivation is obligatory for food handling equipment, for example.
There are stainlessless alloys out there, with less chromium and nickel, still enough to slow corrosion, but not to stop it outright -- COR-TEN brand for example. They might be rated in terms of specified material loss rate under given weathering conditions, and take on a notably brown patina, but survive well for infrastructure (when you don't mind the staining). Hence many bridges, towers, sculptures, etc. made from the stuff.
Basically, you can imagine passivation, or the lack thereof, being a step on the continuum of such a process. 304, 316, 18-8, etc. are on the "negligible" end of the material loss rate spectrum.
Considered in this framing, even mild steel might be acceptable for certain applications, certainly so when the environmental conditions are more mild, or protection is available (oil, paint, etc.), but also where shortdefined lifetime is acceptable given the cost -- automobiles for example.
Regardless of alloy, you need the usual trifecta for corrosion: water, oxygen, and electrolyte. If this is an indoor application in most regions, I wouldn't worry about it, and something like galvanized rod with paint dabbed on the cut end will last ~forever. If condensing humidity is a common occurrence (as can be in some particularly rainy corners of the world, PNW for example), even the salt from ambient dust can suffice to catalyze corrosion, and galvanizing paint or dip might be desirable, or indeed using stainless.
I forget if you mentioned you're in coastal Boston or what. Sea spray, and, say if it's mostly indoors but like a garage regularly open to outside air, that would be marginal enough I'd probably want stainless, and passivation if it should look good or remain hygienic.
Tim