Hmm. It's an interesting, if cynical, proposal. I'm inclined to dismiss it out of hand just because of the cynicism, but I'll take a deeper look at the actual issue.
The two related questions are: (a) would it work, and (b) do they think it would work, to act as the premise suggests?
For (a), I don't think it would work given what we know of Frodo's character, the character of hobbits in general, and the insight into Frodo's frame of mind we are given in the book. Frodo is too far inside his own head to even notice that he is being elevated. He knows he's out of his league, and is made so uncomfortable by it that he isn't encouraged to do anything except hide behind his cushions and listen to a Dwarf talk about local politics.
For (b), I think that if Elrond didn't know Bilbo so well he might think it would work (I think if Frodo were a Man rather than a Hobbit it would likely work very well), but he does know Bilbo and at least thinks he knows something of hobbit culture. I think that Gandalf knows hobbits in general and Frodo in specific well enough to know that this wouldn't work.
It is an interesting proposal though.