A Civil War?

[Voralphion]

Imrahil was teh prince of Dol Amroth and had a legitiment call to the throne of gondor,

I don't think he did. I don't believe he was descended from Elendil, either through Isildur or Anarion/Melendil and so would not have had a claim to the throne of Gondor, or the Princes of Dol Amroth would probably made a claim long before.
I don't think the prospect of the people following Faramir is as clear cut as stated. The people were thrilled at the prospect of having a king as soon as Aragorn had arrived and healed the people in the houses of healing. The people wanted a king to return, and bring back Gondor's glory days, so it is possible they would have accepted anyone with a legitimate claim.
If a civil war did break out however and Rohan did intervene on one side, it would have been to support Aragorn. Eomer had a strong friendship with Aragorn and probably woul have supported him. I don't think the prospect of Faramirs relationship with Eowyn would have been a factor, because if Faramir was as power hungry as he would have to have been to start a civil war, I don't think he could have won over Eowyn.