As a kid, ever shoot a BB gun with bright strong sunlight behind you, low over your shoulder? Can see the streak of the brass colored BB, and how it tends to hook,splice, dive, or rise after a certain distance of travel.
Unpatched ball will gain rotation as it rubs along the barrel, hitting one side or another, and will exit with a bit of spin...but it will be top spin, bottom spin, or some kind of side spin, not the rotational spin of rifling.
Ball will eventually dive off in the opposite direction of the spin.
(odd effect of watching my Nephew shoot air soft...some have adjustable "hop up"..basically bending the barrel to impart a backspin...which tends to LIFT the little plastic balls and gain some range. Can adjust the " hop up" on some makes, giving it more or less. Interresting idea for a smoothbore and not ptach.)
It's how big league pitchers earn their money.
No ball is 100% perfect...can be darned near it before firing, but after a trip down a barrel without a patch, will certainly not be perfect when it esits.
Patch stops the spin...will pick up a bit in flight as even a great patch won't release 100% cleanly each time, with whatever side that hanges up for a micro-second imparting some type of spin.