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A conflict of interest involves situations where the decision maker is conflicted. Not when those that may offer evidence are conflicted. So no, by the definition of a conflict of interest, this doesn't apply.
Instead, the fact that you had filed an EEO complaint against the participating attorney goes more towards the credibility of the witness and the weight to be given to that witnesses testimony. If the judge was not made aware of the EEO complaint against that participant, that would be something that could be raised in an appeal, of the MSPB judge's decision, but it would not automatically negate the outcome. If the judge was aware, or if after being made aware the judge still felt that under the circumstances the evidence weighed in favor of denying your request, the decision could still be upheld.
Just because a person has an EEO complaint against them that does not mean that they are barred from entering evidence. If that were the case, all anyone would have to do to disqualify a witness against them would be to file an EEO complaint against them. What matters here is whether or not the trier of fact (the judge here) was made aware of the EEO complaint. I'm assuming you would have had a representative at this hearing though. It would have been your responsibility to make the court aware of any potential biases in a witness. A witness isn't required to disclose those unless questioned about them.