What does the class action attorney say may happen? If you omit former employment from your resume, your future employers may see the omitted period and ask you to explain. You will need to be truthful, so leaving it off your resume really would not work. See if you can get the employer to sign a written letter of recommendation, so you have that regardless of whether you sue.
If you sue a former employer, whether in a class or individually, that does not mean that you cannot list this company in your resume or not use them as a reference, because the employer cannot tell false information if contacted for a reference. That's where your recommendation letter would be helpful. They can say that you sued them and this is also a public record which your prospective employers can obtain.
Not paying you wages is illegal and hopefully few employers engage in this sort of contact. Also, hopefully your future employers will not take issue with you enforcing your legal rights to be compensated for your work.
Keep in mind that you may be able to help the lawyers prosecuting this case without joining the suit as a named plaintiff (which would show up on public records checks). Specifically, you could provide information to class counsel as a confidential source (this would be non-public), or you could provide testimony as a fact witness in support of the class's claims. If you testified, obviously your former employer would know about it, but your name wouldn't show up as a party to a suit against your former employer.
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Disclaimer: My answer provides information about the law based on the limited information provided in the questions asked and is not intended to provide legal advice or opinions, and does not constitute an attorney-client relationship. The law differs in each jurisdiction and may be interpreted or applied differently depending on the jurisdiction or situation. Accordingly, I highly recommend that you consult with an attorney to discuss the details of your problem so you can get legal advice tailored to your particular circumstances.