For the OP, it looks like it would come down to whether or not disorderly conduct is a crime of violence.
Reasons for Denial of Utah CCW permit
List of the reasons why someone could be denied a CCW permit in the state of Utah.
1.A DUI conviction within the past 6 years.
2.Any Felony conviction (a crime with a jail term exceeding 1-year).
3.Any conviction for a crime involving Domestic Violence in any state.
4.A conviction for a crime of Moral Turpetude (fraud, theft, tax evasion, issuing bad checks, robbery, bribery, perjury, extortion, arson, criminal mischief, falsifying government records, forgery, receiving stolen property, burglary, vandalism, kidnapping).
5.If you have an outstanding warrant for your arrest (a Wanted Person, or fugitive from justice).
6.If you have a conviction for a Crime of Violence, or are a danger to yourself or others due to a past pattern of behavior or threats involving unlawful violence (including threats or attempts of suicide); or a juvenile delinquency in the past 7 years for an offense that would be violent if an adult.
7.If you are the current subject of a Protective Order.
8.If you have any conviction for any offense involving a Weapons Violation.
9.If you have a conviction for any offense involving unlawful use of or possession of Narcotics or a controlled substance.
10.You can not have been adjudicated by a state or federal court as being Mentally Incompetent to stand trial, been committed to a mental institution, or found not guilty by reason of insanity for a felony.
11.If you are not qualified to purchase or possess a dangerous weapon or handgun pursuant to federal law (a Restricted Person).
12.You can not be an Illegal Alien.
13.You can not have been Dishonorably Discharged from the U.S. Armed Forces.
14.You can not have Renounced your U.S. Citizenship.
This list came from the utah-concealed-carry-permit.com website.