Have heard that the disciples of Sri Sannidhi will not chant Gayatri avahana mantra (mantra to invoke Gayatri Devi) during sandhyavandanam. Is there any specific reason for this? Can prapanna-s recite Srirama Charitamaanas?

It does not appear that Sri Sannidhi disciples do not recite Gayatri avahana mantra during sandhyavandanam. Everyone recites the Gayatri avahana mantra that starts with “AyAtu varadA devI..”.
As Srirama Charitamaanas is a bhakti kavyam, prapanna-s can recite it.