Can a property be owned as a condominium if a condo plan has not been filed?

Your answer is a legal one, and best answered by an association-savvy, or at least land-use savvy attorney.

By 'condo plan', you may be referencing a Public Offering Statement, or other document defining land use.

Generally, a mortage lender will require proof of the land-use plan's legal existence -- filing -- before lending money to purchase a condominium unit within the project. You may not be able to hold 'clear title' to a unit if there is no land-use plan filed in the local hall of land-use records.