Sure. But that was not my point - the OP seemed to ask to make them forego attacking Hungary to conquer Anatolia instead. I see no way to speed up the Mongol invasion of Syria/eastern Anatolia enough to ensure they conquer Anatolia before they get to the Carpathian mountains and start thinking of invading Hungary.
If I get it right the discussion is about the Western campaign of the imperial Mongol army headed by Batu Khan and Subuday, which was interrupted because of the early unexpected death of Ögedei Khan.
Well, the point is this army could not invade and conquer Anatolia, no way.
The mission of this campaign was to conquer the territories of Jouchi Ulus (the lands which were granted by Chengiz Khan to the House of his elder son Jouchi, but they were not conquered yet).
And Anatolia was not in Jouchi Ulus. And Iran and Mesopotamia was not in Jouchi Ulus either. Of course they were going to be conquered by the Mongols; actually the whole world was to be conquered. But
later, after the House of the eldest son of Chengiz Khan gets what is his - the Cuman steppe with parts of the Central Asia and Europe.
As for pushing through the Balkans... that's tactical. I mean if Europe was about to get conquered it did not make too much difference which parts of her come first and which parts a little bit later.