Yes. One of the least enforced rules around.
Legally they might be required to register it straight away but the Gardaí usually give a 3 month leeway. Very hard to enforce as anyone stopped can just pretend they're here temporarily seeing that it's not actually defined how long "temporarily" is.
I heard one case where the Gardaí went into the carpark of a huge call centre in Dublin and took down every foreign registration number. 3 months later they did the same and any regs that matched up were obviously not temporary visitors and so were caught.
BTW, I wouldn't mention the word "eyesore" to the Gardaí as eyesores are in the eye of the beholder. Some people would consider any car that doesn't have a 00 reg as an eyesore.