Right, but that's the problem with it. It assumes that there are only two possibilities: no god, or the god of the New Testament.
Betting that Pascal's god exists isn't the safe choice that the wager makes it out to be, because it's equally possible that some other god exists (or just some other version of the Abrahamic god, say Allah or the pre-messiah god of Israel) and your faith in Jesus is just going to piss him off.
Believe in Jesus all you want, but Pascal's Wager is a pretty terrible reason to do so.
Edit to add: Your description is also not even the only possible New Testament god. Some (myself included) would argue that that particular image of god was painted more by Paul than by Jesus.
I don't think so. It isn't concerned with giving any description or shape to the negative case, just an invitation to consider a particular positive case.
There are positive cases for other gospels and worldviews... there's nothing wrong with invitations to engage with one or another.
As science has shown, the truth is best discerned by considering each theory individually (and continually) against evidence. Not "dark matter sounds cool, I think that's true, not MOND" but rather considering each individually for internal consistency and against observation and predictiveness.
"It does not make any difference how beautiful your guess is, it does not make any difference how smart you are, who made the guess, or what his name is — if it disagrees with experiment, it is wrong." --Richard Feynman
If you want to do a fun thought experiment, you might accept that axiom.
If you genuinely believe that an eternal future of unbearable torture hinges on your choice, you might want to cover your philosophical bases a bit more thoroughly.
So yeah, Christianity has some axioms, but it doesn't ask people to merely accept them on faith; that's a mischaracterization. The invitation is to consider (a) how good the evidence really is for your current worldview, and then (b) how good is the evidence for Christianity's truth claims.
Pascal goes one further and suggests considering what you have to gain and lose either way -- which may have been helpful for some when the alternative was mere atheism or unbelief in Christianity, but I disagree that it's helpful in all cases. People coming from Islam have a tremendous amount to lose, including their family, community, livelihood, reputation, and the risk of being condemned eternally by Allah for committing shirk in embracing Christianity, if Islam is true.
I think a better question to ask, whatever someone's background, is "do you want to know the truth, even if it turns out you don't believe it now, and are you willing to follow it no matter what the cost?"
The problem is you can't do this with made up bullshit because the creators of said bullshit can create any number of paradoxes to trap you.
Reality at least has to be self consistent.