Why not if she is applying through CP.
it probably is not impossible to visit, but the risk is pretty high she'll get sent straight home
The OP is the same guy whose Peruvian/Italian GF wanted to enter the USA under VWP with her son and file for AOS.
Plus they prolly won't even ask about immigrant visa.Being an Italian citizen, her probability of being turned back will be slightly less than applicants from other countries.