My thought on it is yes...Sera is/has a spirit. They all do. But with the veil, most are not consciously aware of their spiritual nature and connection to the fade. Only mages, and I guess elves since they still have a cultural memory of magic, can sense these things. But most people are cut off or have forgotten. Especially certian cultures that are very anti magic, like the Qunari or Dwarves.
Sera is different because she has this innate ability to sense energy/vibrations, the fade, spirits,etc. Maybe because she is an elf or because she is a mage who has suppressed her abilities.
She is disturbed by it all, because it isn't the reality she is used to, and she is afraid of the "nothing" -- which I think is a reference to the Abyss. Which, is a place referred to in the game, but also a mystical reference.
Dragon Age, DAI in particular with its spiritual/religious themes, has a lot of mysticism in it, and esoteric dialogue from Solas and Cole.
Whether she is supposed to be connected to the elven pantheon, Andruil or anyone else, I don't know. It might just be a general connection, the way Dagna feels connected to the Titans. Doesn't mean she is also an elven god. She is awakening to her spirit self, and is probably just really freaked out. She's comfortable with her idea of normal and doesn't want to change.
Oh wait, wait! There is a way to explain Danga's connection to the stone imo. And it is not spirit related. I remember there was some codex about how Titans used mindless minions - I imagine similar to those weird blue dwarves from the Descent DLC. From the elven history we know that elves were terrified of what they saw. That "addiction" to the song is not something Solas approves of:
Solas: Do you ever miss life beneath the earth? The call of the Stone?
Varric: Nah. Whatever the Stone - capital S - is, it was gone by the time my parents had me.
Solas: But... do you miss it?
Varric: How could I miss what I never had?
Varric: But say I did have that sense, that connection to the Stone. What would it cost me?
Varric: Would I lose my friends up here? Would I stop telling stories?
Varric: I like who I am. If I want to hear songs, I'll go to a tavern.
Solas: You are wiser than most.
So Dagna's connection is kinda creepy. Suicidial. Does not seem to be like a connection to a spirit/ Just check out what happened to Shaper Valta. She is completely brainwashed.
Itssbloodnow flows through me, and its song fills the gaps in our history. I close my eyes and see glimpses of the world that was, before everything changed and the dwarven race broke in two. Something caused the Titans to fall, and the fate of my people fell with them. The Titan wants me to know. No, more than that. It wants me to understand. There is a loneliness to its song.