If I am not mistaken, even the copper-washed .22 lr bullets are lubricated. The lubricant tends to be a dry type and designed to not pick up 'pocket trash' when used by hunters and plinkers. It still offers bore protection when fired.
The jacketed .17s have no such lubricants and should be treated the same as centerfires. Rust could be a real issue, depending upon the climate you live in and the storage methods you use. In Missouri, I would clean and oil a .17 rimfire after each use in the field - it can get pretty humid around here.
As a side note, I have book in my possession, Small Bore Rifle Shooting, by E.C. Crossman printed in 1927. It belonged to my grandfather, who was an avid target shooter during that period. Most of the target shooters at the time the book was written had not even started using smokeless powder and non corrosive priming yet. Smokeless existed, it was just not considered accurate enough for serious target work. The shooters used target ammo loaded with something called 'Lesmoke,' some kind of mix of smokeless and black and had corrosive primers. Most of the shooting was at 100 and 200 yards. There is a wonderfull 3.3" 200 yard group pictured in the book, shot with Peters TackHole .22 long rifle ammo.
Anyway, there are a few pages in the book devoted to Remington's brand new Kleenbore ammo, loaded with smokeless powder and a new non corrosive primer. The author states, "The samples received by me in October, 1926 were put through a course of severe sprouts. The results , so far as freedom from rust is concerned, amply bear out the Remington claim, except where they concern a considerable length of time, which naturally I cannot report upon....to the writing, however, I have not found ammunition loaded with this primer quite in the accuracy class of the older primer.
This wonderful old book devotes 57 full pages to rimfire ammo and ballistics.