Yeah, it's possible. I seem remember some ancient commentators interpreted it this way, but I can't remember who. I'm skeptical that it can be proven though, given lack of information in the text.

Maccabees is cannon scripture in some churches, but that aside, your answer really doesn't address my question.

@RevelationLad I think we both agree on the assignment of the subjects in the verse, but I don't see the justification for your claim that the Son is the Father's God. I see having a God as being about submission and ontological/functional dependency. But does the Father submit to and depend on the Son? What is the justification?

@RevelationLad I think the verse you cite shows that the Father is the Son's God, but does not show that the Son is the Father's God. The Father says: "therefore God (the son), your God (me), has anointed you...". The Father calls the son 'God' but not 'his (the father) God'

@BenCrowell I don't understand hebrew so my information comes from secondary sources, however this site says the 'l' prefix means 'as', i.e 'as God'. bib.irr.org/was-moses-god-exodus-416-and-71. I'll update my answer accordingly.

My personal opinion is that saying 'Jesus is God' means something different to 'the Father is God', however since your OP stipulates that we assume they both mean the same thing, I've tried to avoid giving my opinion in my answer, and instead answer it within the framework of your stated assumption. I updated my answer to address whether Jesus is YHWH.