Our 18 mos. old son has one, though it was a thing he chose for himself, and actually it's not even just one of anything: at some point, he started taking clean burp rags - which were actually organic cloth diapers - and using them to cuddle. We outgrew having to use burp rags altogether, and he just kept them as loveys.
It's a nice situation for us in that he's not attached to any one in particular: it's not a problem to switch them out for cleaning and there are no concerns of it getting lost. There's simply a stack of them on top of the dresser and he asks or gets one whenever he wants one during the day (usually in the evening as he starts to wear down) and for nap and bedtime. Actually, he doesn't even use it for naps at day care - they don't offer it and he seems to do fine without it. At home though, he knows where they're kept, so he will want one.
I guess I can tell you that it certainly does bring him comfort, and that's always a good thing, imo. And he doesn't seem desperately attached to it that he would have a fit if we went out and he didn't have it. In his specific case, it's not something he carries around all the time. You could give it a try - your little one may not even take to one though. I tried offering a couple of things early on before he chose these himself and he couldn't have cared less for them. Gl!