yes... but then it locks the wheel when it gets wedged between the swing arm and the bolts that hold the sprocket on...
I've seen it happen to an idiot on a Honda 125cc off roader, a week after I pulled over to help him remove said chain from between swing arm and sprocket nuts.
First time I got the chain removed and back on, told him it 'should' be OK to go the 200yrds to his house, but not to use the bike until he changed all the sprockets and chain ASAP.
The thing was so rusted the second time (literally a weeks later) that I poked the split link with my finger nail and it fell apart.
I left him with the chain in his hand and to push it the 200yrds home... Told him if he wanted to sell the bike, give me a call and I'll buy it and fix it up... but it was dangerous in it's (then) current state.
Told him he was reckless to ride any bike in that state and was a danger to himself and everyone else on the road... He wasn't a kid... looked about 35-40... but was a Neath local so that says it all.
For everything that's said to be dangerous if left unchecked, there's a fool that thinks it's B*ll*cks and then is badly hurt when it all goes pete tong!
