She's going to start off suspicious of him, for sure. He's one of the Usurper's dogs, from her perspective. Also, assuming he shows up with Jorah, that complicates matters significantly - but exile or no, Dany has a soft spot in her heart for Jorah, so a little of that might rub off on Tyrion.
Possibly she'll refuse to see him at first, either for the Usurper's dog reason or the Jorah's companion reason, and it might take some heroic act like Tyrion's Nose is talking about just to get him into her audience chamber, but ultimately, she's going to hear him out, and Tyrion can pretty much talk his way out of anything. In this case he'll be talking himself into something, Dany's trust, or at least into her willingness to let him hang around for a bit.
Once she spends a little time with, she'll quickly see what an invaluable resource he is, because Dany is no fool and it will be obvious. Tyrion is generally smart, well-read and, as Tywin put it, cunning, but the biggest thing, as I mentioned in another thread, is that he is uniquely suited to be Dany's advisor on Westerosi politics. Nobody else has his combination of knowledge of the major players and a relatively neutral and disinterested position on everything.
She needs him, and I'm sure he can get that across to her. All he needs is a few minutes in her audience chamber, and he will make it rain.
He'll get her to accept Jorah back into her council, too.