He allowed the return of Eusebius of Nicomedia and Theognis, then banished Athanasius, and then readmitted Arius. Additionally, he was baptized on his deathbed by Eusebius of Nicomedia. It appears as though he changed his mind about Arians and joined them, could this be true?
No, because you are making the mistake of construing 'Arianism' as this kind of unified construct to which Constantine moved towards.
When Constantine summoned Nicaea and they met in 325 they basically hauled Arius' teachings up on the slab, collectively shredded it, and said, "woohoo, great victory for unity". Then Eusebius of Caesarea went away and said, "Yeah, Nicaea was great except for that unity bit". i.e., if you read his letter to his congregation about Nicaea he basically says, "Nicaea is okay but you need to interpret it this way."
Anyway, the aftermath of Nicaea was that Arianism per se was dead. But at the same time the transformed social position of the church vis the Empire, meant that (a) Emperors were a new player on the theological and ecclesiastical chess board, (b) all the players realised that they had some profoundly different ways of approaching the very issue that Arius had provoked.
But Constantine's main goal was unity, and I would say that theological nuances weren't his strong suit. As far as the rest of the eastern church leaders were concerned, Athanasius was a major royal pain in the ***. Constantine had Arius recalled precisely because he thought the whole debate was a bit much and once things had blown over it would just be kind of 'alright' to call him back in from the Principal's office.
Constantine's alignment with Eusebius of Nicomedia is much more political than theological, and it is anachronistic and deceptive to call E of N. an 'arian'.
Sorry if my style is a bit off, I just flew overnight and I'm writing in a hotel room a little out-of-it. Happy to write some more though.
I'm going to start by dodging your question and pointing out that we don't have any contemporary sources on this topic not deeply involved in the Trinitarian/Arian debates.
Some scholars think he went back and forth, some think he never really understood what the debates were about. If we understood more about the dealings of his court we'd understand the intermingling of individuals' influence and doctrine in shaping his thoughts. I think it's fair to say its possible that he became Arian at some point, but it's hard to confirm.