How much reputational value is added to a journal by being indexed in various abstracting and indexing (A&I) databases? I'm co-editing a small communication and media-focused OA journal published by a regional scholarly association. We are in the process of being indexed in selected research databases of EBSCO (just signed the licensing agreement). My question is how does being indexed in EBSCO add to our value as a scholarly journal? As far as I know the publish-or-perish system, the real ground-breaker in terms of being established and respected is being indexed in Thomson Reuters' SSCI or Elsevier's SCOPUS and having an IF. We are still very far from that. Is EBSCO indexing competitive in the current "reputation market", or only good for increasing the visibility of our content? 

Now it had come to my attention that many researchers are pressured to publish in faculty recognized journals. Which, I suspect, may differ from the list of SSCI/Scopus-indexed journals in our field. My question is that how bad the idea would be to write to specific departments asking for approving our journal? We can back up our request by showing that we are internationally recognised, question is how strong an argument of being indexed in EBSCO would be in that situation?
Reputation of a journal matters for two at least two things. The first is whether a library will subscribe to a journal. If you are looking for subscriptions, the more places you are indexed, the better. As your journal is open access, libraries are unlikely to pay money to subscribe, so I do not think this matters. The second is whether academics are willing to publish in the journal. I think serious academics choose journals based on what has been published in the journal in the past. Indexing is like advertising: it might make me think about publishing in the journal, but if everything in the journal is crap, I am not going to publish there.

As for faculty recognised journals, this sound fishy to me and I hope you are not talking about mainstream Western universities. Presumably, in these crazy faculties, if a researcher thinks your journal is good quality, they will fight to get the journal recognised regardless of where it is indexed.