Syphon, alright. But I'd surmise that Littlefinger is behind Waters, not the Tyrells nor Lannisters. Remember that Littlefinger wanted certain Targaryen tapestries from Cersei? The value of pictures are their ability to convey visual details of the past... i.e. Targaryen physical traits.
Why would anyone send a fake Targaryen to Dany? Political power. If someone could convince Dany that Aegon was alive, then Aegon would be the real king, not Dany.
I'm not so sure that the ploy directly involves Dany. Dany has little actual power. Okay, fine, she has the Unsullied and growing dragons, backed by freed slaves. But Westeros has knights, hedge knights, men-at-arms and not to forget forces such as the Alchemists and the Maesters. Most people still see the dragons as still being an old wive's tale, something that sailors heard while on the way and under the influence of alcohol. If they heard it at all. Westeros is big. Littlefinger might be keen on harnessing the power of the dragons, but I believe that he would stand more to gain by presenting a fake Targaryen to the war-torn country to reestablish peace.
They want peace, that's for certain. Why would people choose for the Targaryens over all the other options? Perhaps they don't need to. They can rule together. Aurane with Cersei or Marjory, for the eyes of the people, of course. Yet, I can't escape the feeling that Petyr might set up a marriage between Sansa and the fake Targaryen, giving him indrectl influence on the people that would flock to the Targaryen banner. That is, of course, only in the case of Petyr being the one who puts forward another pretender to the throne. And a rightful one, to be sure. Well, as rightful as an impersonator can be. Perhaps the words in this case do not mean the dragon being a mumer, being fake, but the dragon OF a mummer. You know how Petyr likes to play his chess-games. Perhaps it is the same?
But one last thing remains before I end this post and go to sleep:
How do they present him? Whomever presents Aurane must certainly have some backstory prepared. You know, something that's not along the lines of "This is Aegon". "I heard he was dead" "He got better". That would be horrible. They can hardly go about saying that they found him under a bed in the castle of his birth, now can they?