The simple answer is no.
The Lubavitcher Rebbe wrote a letter about this in 5704 which was printed many years later in the first edition of the Kuntress Torato Shel Moshiach.
In that letter, the Rebbe brought many of the citations brought by Rambam from Shas related to different activities that Moshiach is engaged in and how they fall out chronologically. He also demonstrated with related sources that some pertained to Moshiach ben Yosef and some pertained to Moshiach ben David.
The Rebbe then noted that in the Mishneh Torah, Hilchot Melachim, Rambam does not mention explicitly the terms Moshiach ben Yosef or Moshiach ben David, but uses the innovative terms of Presumed to be Moshiach and Moshiach with certainty.
The Rebbe points out that this is in spite of the fact that Rambam was certainly familiar with these traditional distinctions.
At the conclusion of that letter, the Rebbe writes that from this it is concluded that the view of Rambam is that Moshiach ben Yosef and Moshiach ben David are speaking of a single individual.
For what it is worth, this conclusion of the Rebbe also seems to be supported by the plain meaning from the Prophet Yechezkel 37:15-28 that is read as the Haftorah to parshat VaYigash.
For more detailed discussion of this subject, see the following: https://judaism.stackexchange.com/a/59634/7303