The CL works with no batteries. Only the meter would be non-operative. The spot meter is a nice feature of the CL, in fact what I'd consider a major point in it's favor, but a CL with no meter is still a CL, and as such, a very nice camera to use. There aren't many options when it comes to compact M-mount bodies - make that NO options.
That said, the CV bodies are slick pieces, and seem to hold value far better than I'd prefer (I'm either poor or cheap lol). IMHO they cost what they are worth, and the fact you don't see used CV bodies going for a fraction of their new price is a testament of their very real value and quality. Personally I'm always torn between a CV body and a good CL. The rangefinder base is comparable, but the CL metering and shutter dial is the trump card for me. I suppose at some point I will have to own both a CL and CV body.
As has been said, an M mount Bessa is a better thing unless you already have LTM lenses or an M mount body. IMHO, being restricted to LTM lenses is like being restricted to dating former supermodels - you are doing fine if that's your only limitation

But being able to mount M lenses as well with a single LTM-M adapter is a better situation, all else being equal. Just tack US$50 to the price of an M-mount Bessa.
Realistically, tack US$50 per LTM focal length you own if you go with the CL, since the Bessa's have manually selectable framelines making the "right" adapter a foolish expense. (That makes a mountain out of a molehill, don't let "improper" framlines stop you from buying a camera. I dislike extraneous framelines as much as the next, and the CL only has 40mm always visible, with the 50mm and 90mm depending on the lens mount. Just go with the smallest frame in the finder. 50mm is slightly smaller than 40, and 90 is slightly larger than the rf spot.)
IMHO, buy a CL if you want a very compact body for LTM or M lenses. Go with a Bessa if you want a cheaper alternative to an M body. The CL has a spot meter, which if you never used one in a camera sounds like a meaningless distinction. The CL is worth it just for the small size. Paradoxically, if you like fast lenses the Bessa is probably better from a handling standpoint - the CL is a small body that is easily over-balanced by a large lens.