It is illegal to sell a UK registered car in this state. A purchase invoice is one of the required [broken link removed] now for the revised VRT procedure as carried out by NCTS. The website that didn't have that detail probably hasn't updated their content since NCTS took over this function.
If the car has been in the state for more than 7 days, the current owner has already failed to fulfil their requirement to register for inspection.
If the car has been in the state for more than 30 days, an additional charge may apply. Revenue or the Gardai can also detain the vehicle.
Personally, it's just ringing too many alarm bells. I wouldn't touch it.
Leo