Is it legal to mortgage the real estate license without paying the property management fee?

Legal. But if you don't pay the property fee, the property can sue you.

Real estate under any of the following circumstances shall not be mortgaged:

Real estate with disputed ownership;

Real estate used for public welfare undertakings such as education, medical care and municipal administration;

Cultural relics protection buildings and other buildings with important commemorative significance;

Real estate that has been announced to be included in the scope of demolition according to law;

Real estate that has been sealed up, detained, supervised or restricted in other ways according to law;

Other real estate that may not be mortgaged according to law.

References:

Article 8 of the Measures for the Administration of Urban Real Estate Mortgage