Yes, he could have appeared.
Aragorn was being fostered in Rivendell at the time Bilbo and the Dwarves visited, and the material covering this is allowed to be used in the movies, so there was absolutely nothing to stop Jackson & co from having him there.
However, you need to remember one important point. There is a third movie still to come.
On Bilbo's return journey he also visited Rivendell, as is noted in Chapter 19, the Last Stage:
It was on May the First that the two came back at last to the brink of the valley of Rivendell, where stood the Last (or the First) Homely House.
Here, Bilbo and Gandalf stay a while at Rivendell, and
When the tale of their journeyings was told, there were other tales, and yet more tales, tales of long ago, and tales of new things, and tales of no time at all, till Bilbo's head fell forward on his chest, and he snored comfortably in a corner.
Bilbo stays a week, frolics a little with the Elves, and finally leaves:
Weariness fell from him soon in that house, and he had many a merry jest and dance, early and late, with the elves of the valley. Yet even that place could not long delay him now, and he thought always of his own home. After a week, therefore, he said farewell to Elrond, and giving him such small gifts as he would accept, he rode away with Gandalf.
The point I'm making here is that just because Aragorn wasn't in the first movie, you shouldn't assume that he's not going to be in the Hobbit movies at all. The two events I quote here (tales and frolicing) provide examples of where he might have been present, if needed.
So if Jackson wants to include him as a thematic link to LotR, the third movie would seem a more logical place to have him included, so that Aragorn's story can run from the Hobbit movies to the LotR movies without interruption in the form of Bilbo's adventures.
Update - 23rd December 2014
And he was included, but in name only.