If you have a job lined up no. If you're going to be job hunting wouldn't you get backdated unemployment even if you had the savings to live without it?
For context, depending on the state, unemployment can be a few hundred dollars per week. So you might cover the costs of your lawyer. No idea of the answer to your question as there's also an assumption you're looking for employment while unemployed and may be ongoing documentation requirements.
Depending on your state, hiring a lawyer might not be necessary. In at least one state, the employment division takes violations of employment contracts very seriously and will go to court on your behalf if the violation is egregious enough.
And in all states, you don't have to have a lawyer to bring a case. These are civil cases, and you can represent yourself. You're trading time for money in that situation, of course, and there's a learning curve you need to mount.