The simple answer: Nope!
Currently you can summon these pets on any toon (regardless of faction), but unless you've purchased the Argent Pony Bridle for the Argent Squire/Gruntling on the toon you're summoning the "pet" on, you won't have access to his additional mail, vendor, and banking features.
The Guild Herald and Page are in the same boat as the Argent companion. Unless you're on a toon that's in a guild, the vendoring aspect of these two pets won't be available to that particular toon. You can still summon them, but they will just be humanoid companions without any additional vendoring ability.
Side note: I'm still not sure if we'll actually be able to summon cross faction pets once MoP goes live. At the moment, I can summon my Argent Squire just fine while on a horde character on the beta. This might be changed in a future build, though. We'll see.
I'm also unsure if you'll be able to "use" these companions' additional features if you DO meet the requirement(s) but they're of the opposite faction. Asking an alliance Guild Page to sell stuff to your horde character seems kind of strange. And how on earth do you coax an Argent Gruntling to accept a Pony Bridle that was purchased from and meant for alliance lol?
Fun fact: If you do summon a cross faction pet and try to talk to him, the speech will be jumbled jargon. Very fitting and amusing!
I'm not sure whether or not I'm for or against being able to summon a horde pet while on an alliance character or vice versa. I think it's pretty interesting for RP purposes (I'm thinking something like, "I captured this alliance and now he's my prisoner of war!" lol), but it does feel a bit out of place at the same time.
It also puts pressure on collectors to create toons for the "other side" just to collect a companion. Not everyone is against jumping through hoops for their collections, but some might feel disgruntled about having to level up to the appropriate level for the Argent pet and reputation grinding with a second guild to acquire the Herald and Page.
But to each their own! Personally, I'll be working on my alts to gather as many pets as I can, regardless of faction.
PS: For those who already completed the pet collecting achievements on one toon, you'll be able to summon the reward pets (such as Nuts) on all toons in MoP. This is due to the fact that the completion of these achievements will be cumulative across all your characters.