The only downside to waiting to file your discrimination suit is the issue of timing.
If the mediation does not happen until three hundred days after the discrimination event, you will be barred from filing an EEOC complaint. At that point, you will not have any leverage over your employer. You will not be able to threaten it with a lawsuit because you will be beyond the required time limits for filing the legal complaint.
While unions may discourage it, you may want to file the EEOC or other complaint before the time period expires so that you can protect your rights. Then, once you’re in mediation, you can offer to drop the charges once you reach an agreement.