I doubt it would have any affect at all as they may have had a passport anyway for travelling outside the EU.
The reason VS is so popular with EE girls is because many don't have EU passports. Romania hands out ID cards to almost anyone from the EE, but not passports. Bulgaria is similar. So you get a lot of Albanians, Serbs, Macedonians and other Yugoslavs, Ukrainians, Moldovans and others who would otherwise be excluded from the EU, getting in using Romanian ID as a back door.
Its why AW stopped accepting ID cards as verification around three years ago, forcing the girls to switch to VS
Of course a lot of legit girls just travelled on ID cards as well - passports are just another expense for them