Sorry to again have to refer to the company policy in this matter, but if they would count a verbal acceptance nothing in law is going to make that invalid.
In law, nothing about a verbal acceptance is less formal than a written acceptance. Many people believe that for something to be formal, it has to be writing. That's actually not true. Lawyers push for things to be in writing, not for the formality, but so that everyone agrees on what they are agreeing to. Having it in writing just gives better proof, but there is no legal need for something to be in writing for it to be legally "formal."
The problem that you are ultimately facing here is that the courts are going to err on the side of the employer. Unlike a right that you might have, like the right to unemployment benefits
, where the state would lean in your favor, severance is not a right. It is a benefit offered by the employer and the state court would always be leaning in the direction of the policy set out by the employer, because they are offering something that they are not legally required to offer.
So, any sort of ambiguity is going to be interpreted in the favor of the employer here. You would have the burden to establish that you were owed severance (not them having to prove that they didn't owe you).
So, the court would have to see some definitive statement in the company policy on severance which indicates that you are only disqualified if you sign a written acceptance, rather than a verbal acceptance.