I was given accelerated rehabilitation for a misdemeanor charge, will the arrest show on a employment background check

It will show as a pending case. Yes, they can refuse to hire you. If given the opportunity, explain that the charge will be dismissed and that you have no convictions.

Now, if the arrest was properly entered into the database, was not expunged or sealed it will show as an arrest. Also, you must know that the arrest per se is not an evidence of any crime, yet depending of the type of employment and the employer, once the background reveals the fact of the arrest that may be a factor in determining your eligibility for that position.
If I were you, I would look into expunging the arrest record in CT, if you stand statutorily eligible for that relief as a first time offender after successful completion of the unsupervised accelerated rehabilitation. Please inquire further with a local criminal counsel.

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