I don't think that it will be that simple. Firstly Tyrion is part of the family that killed her brother's children(we all know how much she despises the Usurper's dogs), also we know that Barristan bears no great love for Lannisters as well. The fact that he's keeping company with Brown Ben is also going to work against him I think.Also I dont think her prickly nature will allow her to to tolerate his satires.
Then theres this interesting passage in ACoK
Does this foreshadow Viserion taking a liking(being the most docile dragon) to Tyrion or perhaps even killing him?
The cream-colored dragon sunk sharp black claws into the lions mane
Either way, I don't think their meeting will go as smoothly as many people expect.