Yes it it important to stick it out to the end with EEO. One tactic of managment is to scare you into submission, then to fire you. The Union does its best, but with bullying or harassment, the grievance process is not designed for multiple charges over a short period of time. EEO is really the best process for harassing manager(s). The only downfall is that it must be discriminatory. If not, there is really little recourse.
However the good news is that even a weak discrimination complaint can turn into a rock solid retaliation complaint. It pays to file early and fast. No value in delaying in hopes of an early settlement.
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