Yes. Unlike certain advanced Sri Vidya mantras (like the Panchadashi), the Virutham is a stotra (hymn of praise). It can be chanted by anyone, regardless of gender, caste, or initiation status.
Madhipoala oliyuthra pughaz nedum karamudaya madha gajanai yeendra thaayae... Azhaghaana kaanchiyil pughazhaagha vaazhndhidum ammai kamakshi umaiyae kamakshi virutham lyrics in english
Kamakshi Virutham is a powerful hymn that is believed to have spiritual significance. Reciting the hymn is believed to bring blessings and prosperity to the devotee. The hymn is also believed to have the power to grant liberation from the cycle of birth and death. regardless of gender