Technically yes, although that might not stop him/her from summoning other Fakes.
It depends on whether everybody else has summoned yet, and whether Caster is either (1) Medea or (2) somebody who can pull off the same level of magecraft as Medea.
This is an AU, so theoretically you might see a Caster capable of pulling off a Fake Servant summoning. Depends on whether Ryuunosuke is feeling experimental that evening, I guess. Because if the serial killer summons Gilles, there's no way that Team Kuuru can summon anything except Cthuhlu.