Whether or not you have to pay the attorney's fees of your employer depends on the type of relief requested by their attorney's during the course of the case and what, if any relief was granted by the judge/administrative body/etc. If the EEOC did not issue a determination and merely terminated their investigation because the 180 deadline has passed, that does not necessarily give any indication on your chances of winning. As mentioned by the prior commentor, you should discuss these issues/questions/concerns with your attorney--if nothing more than to get your money's worth. Good luck!
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Since you have an attorney, you need to be asking your attorney these questions. We are not here to second guess retained counsel.
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If all you did was file an EEOC charge the answer is "no" and the employer's attempt to collect then may create a case for you all by itself.
The EEOC lacks the resources to investigate fully the charges that are filed. I would not place much weight on its dismissal.
You should get a free consultation from a qualified lawyer .