Can I port an autocomplete rule from one environment to another?

Yes, you can using the standard Customization Set Migration (CSM) process. Rules are also migrated as part of the P2T migration.

However, you can't migrate a rule from one sandbox of an environment to another sandbox of the same or different environment. You have to manually recreate the rule in the new environment. Also, note that when migrating the rules using CSM, any direct or indirect reference to IDs will be blanked out if the given reference entity is manually created in the new environment and not carried over by P2T.

For example, if the rule references a location either in a condition or default assignment by using the LOV selector, the corresponding ID associated with the location name or code in the UI is used. If this ID is different in the source and target environments, then the selection will be blanked out in the target environment. You have to manually edit the rule and reselect the name or code from the editor to reference the new ID in the back end.