Short answer: yes, and you almost never need to. If you've been pulling your rear wheel every time you clean your chain, that's extra work for no benefit — unless you're actually replacing the chain and sprockets, the wheel can stay exactly where it is.
The wheel was never the problem
The part of the chain you need to reach for cleaning is the exposed lower run — the stretch hanging between the front and rear sprockets, underneath the swingarm. That section is fully exposed whether the wheel is on the bike or sitting on your bench. Pulling the wheel doesn't expose more chain to clean. It just adds a step you didn't need.
The whole reason a wrap-around brush design exists is to work on that exposed run with the wheel in place: it wraps around the chain, you rotate the wheel by hand, and the chain feeds through the brush a link at a time until you've been all the way around the loop.
When you'd actually pull the wheel
Replacing the chain and sprockets is a different job. You're cutting the old chain and removing it entirely, which usually means pulling the rear wheel for access and to reset tension once the new chain and sprockets are on. That's a teardown, not a cleaning. If you're degreasing, scrubbing and relubing the chain you already have, there's no reason to get anywhere near that far into it.
How a wrap-around brush makes wheel-on cleaning easy
Get the bike on its stand, put the transmission in neutral, and rotate the rear wheel by hand while the brush stays wrapped around the chain. The CC360 scrubs all four faces — both side plates, the roller faces and the inner edge — in one pass, so you're not fishing a flat brush around behind the chain to reach the side facing the swingarm. That's a real limitation of flat-brush designs: half the chain is turned away from you at any given moment, and you have to work around it.
One safety note that applies here regardless of whether you have a stand: never rotate the wheel by starting the engine and putting it in gear. Turn it by hand, or use the rear brake to hold tension while you turn it with your foot on the tire.
No stand? That's a separate question
Not having a stand is a different obstacle from not wanting to pull the wheel — you can leave the wheel on the bike and still need a way to get it off the ground or rotate it without a paddock or center stand. We cover the roll-forward method, the side-stand method, and that same engine-in-gear safety warning in more detail in How to Clean a Motorcycle Chain Without a Stand.
Quick answers
Do I need to remove the chain to clean it?
No. Cleaning is done on the chain as installed, on the bike, with the wheel on. Removing the chain, or the wheel, is only necessary when you're replacing it.
Will leaving the wheel on make it harder to reach the whole chain?
No. The chain is a closed loop, so rotating the wheel brings every link through the same exposed section you're cleaning. You reach all of it without removing anything.
What if my bike doesn't have a center stand or paddock stand?
That's a separate issue from the wheel. See our guide to cleaning a chain without a stand for roll-forward and side-stand methods — the wheel still stays on the bike either way.