Yep, financially I may end up better off in the short term, between the severance and unemployment. But it wasn't a layoff, it was a termination. So that is going to be a lot harder to deal with for explaining to future employers I would think.
When you apply for future jobs you are under no obligation to go into the details of your departure from this one. I wouldn't recommend lying, but you can certainly phrase it differently than "I got fired". Especially since you were already looking for other jobs, you can legitimately say that you felt the role was a poor fit and you started looking for something new.
I've had to sign one of these to get cashed out after a company-wide lay off before. I ran it past a lawyer friend and he says they do not hold up in court.
Saying that, there are plenty of ways to frame the situation without being overly negative about the former company or yourself.