Moshe made everyone drink from the ground-up golden calf waters (Sh'mos 32:20). Did he force the Levi'im as well?
Rashi cites the Gemara in Yoma 66b that there were three levels of those who sinned that day. The drinking was applied to those who sinned without warning or witnesses (according to the opinion that Rashi cites). The Gemara in Avoda Zara 44a says that he was checking them like the law of a Sotah. The implication is that this was only applied to those that Moshe suspected. So your answer will depend on whether or not Moshe would have suspected the Levi'im.
While it is true that the Gemara derives from an immediately following verse that none of the Levi'im participated (Yoma 66b), there are indications that the Levi'im had a higher level of commitment even before then. One example: The Ramban to Shemos 5:4 explains that the Levi'im were not included in the decree of hard work because they were the elders and sages of the people. The Da'as Zekeinim there explains their exemption from the hard work to be a result of their devoutness. So it is possible that Moshe did not have reason to suspect them, as they were already established as more devout.
The drinking happened several pesukim before shevet Levi joined Moshe, so it seems that the Levi'im were no different than the others at that point.