And to answer your question...perhaps.
There are a variety of ways to track down prior arrests records. Your name/date of birth/social security number and your fingerprints all can flag arrest records.
This is a great webpage that covers Missouri records checks
From that page, this paragraph:
Q: What is the difference between open and closed records?
A: Open records include convictions, pending charges within 30 days of the arrest, and suspended imposition of sentences
during probation. Closed records are those records when the accused is found not guilty, charges were nolle prossed or dismissed, suspended imposition of sentence after probation is completed, and arrests after 30 days where no charges have yet been filed or reported by the prosecuting attorney. Open records are available to anyone who does a record check on someone. Closed records are only available to oneself, the sentencing advisory commission, law enforcement agencies, prosecutors and court
personnel, child care agencies, the Department of Revenue, in-home service providers, the Division of Workers' Compensation, criminal justice
employers, child care employers, nursing home employers, and to federal agencies for such investigative purposes as authorized by law or presidential executive order.
SO, looks like your record is an open record and would be available
Now, if you want to change that, you should consider applying for expungement
This may help you in the future.
Please let me know if you have questions else please hit the green button, its the only way i get paid