Are the Elements Connect fields compatible with Jira's import/export?

Yes

Issues with Elements Connect fields can be copied from an instance to another with the native Jira "Export to CSV" and "Import external system" features.

The only conditions is to have the same Elements Connect fields configuration on both instance (or, at least they must be compatible > store the same value as Issue key).

Related article

CSV Import - How to set Elements Connect field when creating issues from a CSV file