Generally speaking, yes. Anything that is filed through the court system is going to leave electronic records as well as copies of paper files and records in various places. The proper question to ask would be:
Who can see it; and what can they see?
First of all, Minnesota Court Rule 4 says that Domestic Abuse and Harassment records are not accessible remotely. This means that any records maintained by a court administrator in relation to an Order for Protection (OFP) hearing or a Harassment Restraining Order proceeding are only accessible if searching on the courthouse database, and not accessible when searching outside of the courthouse. This accessibility policy includes any documents associated with the OFP hearing, except for medical records, exhibits, or items subject to judicial orders. See Minn. Ct. R. 4; see also Minn. Ct. R. 8, subd. 2(d)(1).
One exception is where an OFP is pending, and there has not been an Ex Parte OFP ordered. In this case, the fact that an OFP has been filed against you is not accessible regardless of where the search is conducted. Meaning that an employer would not be able to see a pending OFP filed against you.
However, all of these records are discoverable by law enforcement, court administration, and government personnel in relation to conducting an investigation, enforcing an order, or service of process.