I also think Eowyn would have met Faramir, if the War had been successful. An alliance between the first Lady of Rohan and the Steward of Minas Tirith would have been seen as something very beneficial to fostering good links between the countries. Eowyn would certainly have been paraded among the men of Minas Tirith by her brother - who would have done it out of love, a wish to find her a good husband...before anyone gets outraged and tells me Eomer would not be so rotten.
The question is would Eowyn wish to hand over the Stewardship of Edoras as quickly as Faramir was willing to hand over the keys of Minas Tirith to Aragorn? Methinks Eomer might not have had an entirely easy time of it.