question
Does an arrest for an offense with no subsequent conviction "show up" on a record search?
In theory, yes it should. In practice, the answer has to be maybe.
The National Crime Information Center (NCIC) is the United States' central database for tracking crime-related information. It links to systems in all 50 states. In order to understand and interpret criminal histories and NCIC records, I went through some training with MN's BCA (Bureau of Criminal Apprehension). In theory, all information, arrest, charges,
each[ court appearance, conviction and dismissed charges, and sentence, are accurately recorded and can be tracked.
In practice, the system is dependent on data input and that has been unreliable. Often times in investigating a prior charge you may find arrest, charge, 1st court appearance - then nothing further. What happened after that? Well, nobody entered the data, so then you resort to researching the actual court files in the jurisdiction of the offense. Very old school.
So, an arrest is recorded and can be found on a full record or background search.
Related but a different system, the National Instant Criminal Background Check System (NICS) is so that any FFL may contact for information as to whether the receipt of a firearm by a prospective transferee would violate Title 18, United States Code (U.S.C.), Section 922 (g) or (n) or state law.
http://www.fbi.gov/hq/cjisd/about.htm for info about these systems.