Well yes and no. Puyi certainly wanted to be reinstated as the true emperor of China. So much so that he had the Qing coronation robes moved from Beijing to Changchun in 1932, the capital of Manchukuo. Of course a full restoration of the Qing Empire was not on the table. The Japanese Empire established a collaborationist government with the KMT defector Wang Jingwei. While they did collaborate with the Japanese, their primary goals were maintaining a strong "republic" and combating the Communist insurgency. Much like the Japanese, they too were wholly opposed to a full restoration. One thing to note here is that some Japanese advisers, both political figures and military figures, often dangled the prospect of a full restoration in front of Puyi to entice him into collaboration, but no real plans ever really came close to fruition in this regard.

There probably were people wishing for a full restoration of the Qing Dynasty in Manchukuo, but I am not aware of any specific movements during the Manchukuo period. Given the strong Japanese military presence in both Manchuria and East China I doubt there would have been much of an opportunity.

There was however the 1917 Manchu restoration, which lasted about 11 days and was quickly thwarted by the Republic of China (ROC) troops. There were significant number of Manchu soldiers, mostly led by ex-bannermen, that rallied to the cause and there were demonstration of support for the restoration. I don't know how many Manchu soldiers were involved and from the primary sources I've read it wasn't clear at the time either.

This would be the last major attempt to restore the Qing Dynasy. Although, Puyi would not be expelled from the Forbidden City until 1924 when his imperial titles were officially revoked. Puyi and his advisers discussed the possibility of a restoration for years and negotiated with various warlords involved in China's civil war. Nothing ever came of these plans until the Japanese invasion of Manchuria in 1931.

Truthfully, Manchukuo as a nation occupies a strange place in history. It was on the one hand a restoration of an old dynasty that was legitimized through traditional Confucian logic, and yet at the same time it was a pan-racial, nation state. Puyi was not an emperor but rather a chief executive, much to his frustration as he wanted to rule under the Mandate of Heaven and not as a nationalist political figure.

Ultimately however, Puyi was simply a figurehead under the Japanese to project a sense of legitimacy, both to the Manchurian population and the rest of the world. It was very much an attempt create an illusion of self-determination and Manchu nationalism. Given this sort of vague political environment, it would be challenging and strange to launch a popular mass movement to simply alter the title of Manchukuo's ruler.

The best book by far on this subject is Prasenjit Duara's Sovereignty and Authenticity : Manchukuo and the East Asian Modern.

Interestingly though, there was a minor revolt in the late 1950s during the Great Leap Forward/Great Famine when a local peasant led a minor movement against the PRC to restore the monarchy. It was isolated to a single village and I've only ever read one reference to it in Tombstone by Yang Jisheng. It's possible that the reports were all based on hearsay. That's the most recent such movement that I've heard of. I'll need to go find my copy of the book to check the exact year/location.