Steven pointed you in the right direction. Best of luck
Statements posted on the Avvo Q&A section are not legal advice. No prudent person anywhere at any time should ever rely upon any statements posted on the Avvo Q&A section. There is no attorney-client privilege based on this interaction. I am not your attorney and there is no attorney-client privilege up until the moment that we have a signed engagement letter with a clear understanding regarding fees - at which point we will not be discussing your legal issue online on a public Q&A board that anyone in the world can view. You should find an attorney that can best represent your interests: using the Avvo lawyer search is one of many possible utilities online to collect names of lawyers you might be interested in meeting with offline to discuss your legal issue in full detail so the legal advice can be tailored to the specific facts of your legal issue.
From our perspective as criminal defense lawyers, the answer is clearly no. However, the standard used by employers is not necessarily the same. I did a quick check and saw a pretrial diversion program for certain offenses involving trustworthiness bars employment with the FDIC: http://www.fdic.gov/regulations/laws/rules/5000-1300.html . I think you are going to have to see the individual agency's rules. This question would be better asked in a different forum, probably employment law.