This was a question that we brought up in our local game store. So what do you think?
As pertaining to a paladin's divine bond ability, I'd have to say no; similarly, a druid's animal companion can't also be used as a familiar (in the case of druid/wizards out there). If this were allowed, an eidelon would also get the benefits of an animal companion and gain the celestial template when the paladin is 11th level. I'm for keeping animal companions/eidelons/familiars/etc. seperate entities.
That said, I don't see why the eidelon can't be used as a standard mount, as long as it's a size category larger than the rider.
I agree with Rhys. It is difficult to combine the rules for eidolon and mount.
If it was me, I'd just take the divine bond with my weapon, and make the eidolon as some celestial-ish being that I can use as a mount.