Can I pass a background check with a withheld adjudication?

It may depend on several things, none of which is revealed by the question:

(1) What was the original offense or charge?

(2) What was the sentence?

(3) Did you successfully complete the terms of the sentence?

Since "adjudication withheld" means different things in different court systems,

(4) if #3 is 'yes,' what was the judge's final ruling in your case? Was it dismissed, or what?

Finally:

Unless the arrest, the charge, and the court action was EXPUNGED, your offense will appear on a background check.

Depending on the factors set forth above, if the employment questionnaire asks if you were ever CHARGED or ARRESTED you must answer yes, or risk having the employer think your are trying to conceal it.

If the background check is being conducted by a government agency (for employment or for a security clearance) it will make no difference if the record was expunged or not. Expunged records are accessible to background checks conducted by government agencies.