Yes and no (!) The cartridges are supposed to be headspaced at the case mouth the same as in an automatic pistol. If the cylinder has been correctly chambered you can shoot without the clips and dig out the fired ones with your fingernails.
But if the chambers are too deep the round may drop far enough so it doesn't fire. Not likely, but it has happened. I would experiment by trying it with the particular revolver and see what happens. No, it won't hurt anything, but take something with you to knock out the cases.