I hate to give you a non-answer for your very interesting question; however, there is little proof that the early Ilkhans were Buddhist merely because they wanted the favor of the Great Khan Kublai. It is an interesting topic you bring up though for multiple reasons, one reason being the complexity of the expedition that Hulagu had been sent on in Persia and the Middle East. You see, it is thought that initially the Great Khan Mongke sent Hulagu as a commander of a military intended to conquer the region and eventually return to Mongolia, this implies that Hulagu was not sent to be the ruler of the region showing some factionalism even among the sons of Tolui, which Hulagu was, and so was Mongke, and of course so was Kublai. This is mostly made evident by the fact that a letter was sent to King Louis IX of France, this letter is in the Vatican archives and Hulagu calls himself dux milicie Mungalorum which is commander of the Mongol military. Some sources claim that Hulagu and Mongke had a pre-arrangement where Hulagu was going to eventually be given the Ilkhan title but hid it at first to not anger the other houses. It’s worth noting that Ilkhan can essentially translate to “lesser” Khan, but not in the negative connotation of the word lesser, for the Mongols loyalty was important so this was actually an honorary title, I’d think of it as a Viceroy position but with the Toluid Civil War they end up ruling the region though they pay some lip service to Kublai Khan.

Well, what does all of this mean you might be wondering. What this means is that the situation in the lands that will be the Ilkhanate was very complex and your theory of being looked upon favorably by the Yuan is a possibility, but again…there is little proof; however, I like where your mind is going with this because although Hulagu and even his son Abaqa were known as Buddhists, it seems they still held on to their Shamanistic beliefs, proof of this would be seen once Hulagu had passed away in 1265 and an animal was slaughtered, a common Tengri practice. Once Hulagu passed away he was succeeded by his son Abaqa (who did recognize Kublai as the Great Khan of the Mongols), and once Abaqa had passed on in 1282 he was succeeded by his brother Tekuder who was baptized as a Nestorian Christian but eventually converted to Islam. His reign was very short as his conversion angered the other Mongols and he was quickly overthrown by Arghun, his nephew, who was known to be quite the serious Buddhist. Arghun sought help from Kublai in this dispute and although Kublai was angry at Tekuder for his decisions, he was simply too far away to send support. This is to change in 1295 when Ghazan Khan finally declares his conversion to Islam and goes through a state of reforms one of which was to expel Buddhists out of the lands of the Ilkhanate.

In short, we can’t say for sure that the early Ilkhans professed Buddhism for support from the Yuan, it’s very possible at least from a political standpoint, but it’s also really tough to know as Mongols were very ‘humble’ in accepting religion and perhaps Hulagu just liked Buddhism but wished to continue practicing his ways as well. The Muslim sources are also a bit unsure of this as they typically didn’t seem to care one way or another because whether they were Shamanistic or Buddhist they were still pagan in their eyes, which leads me to my final point – perhaps the early Ilkhans made sure to stick to Buddhism or Tengrism to keep themselves separate from the local populations.

Again, I apologize for this answer-nonanswer style, but simply telling you no or maybe isn't going to help you, me or anyone. I did want you to understand that this was a particularly complex situation from the very beginning, especially do to the rivalries between the different Mongol houses.

The Mongols, 2nd Edition David Morgan

Power, Politics, and Tradition in the Mongol Empire and the Ilkhanate of Iran Michael Hope, Oxford University Press

The Mongols and the West 1221-1241 Peter Jackson