Well, the idea is that Celegorm and Curufin are fleeing westward from their holdings in... Himlad? Himring? Call it a chance meeting on the surface, though quite obviously more opportunistic than that; basically Orodreth would be placed in their debt. During the eight years they are in Nargothrond, Celegorm and Curufin would slowly gain power, and according to the published Silmarillion, they lead a sizable contingent of the military arm of Nargothrond and proven useful. Essentially they could control Nargothrond's future through Finrod's only heir, Orodreth (as indeed they do until word comes of the death of Finrod).Meril would have had the opportunity to meet Lúthien at Galadriel's wedding in Nargothrond, or possibly at the Mereth Aderthad. So, yes, a Sinda who looks up to Lúthien as Thingol's daughter and a leader of Doriath fits the character we have given Meril thus far.
She is quite protective of Orodreth. She knows he was deeply hurt by the loss of his parents. He was leary to even start a family after the death of his mother in the Dagor Aglareb. She wants to support him and help heal him. So, leaving Orodreth while he is facing a major crisis would be out of character for her. My presumption is that she will urge Gil-galad to leave, but will stay behind herself.
We have not yet come up with a firm answer to the question of what Celegorm and Curufin are doing in Nargothrond. Having them aid those escaping Tol Sirion fits, but...why are they on hand for that? We need to tell a story that puts them there if we are going that route.
I am fine with using a flashback to the end of the Dagor Bragollach to explain their presence in West Beleriand, but we are supposed to use flashback only very sparingly as a narrative device.