No. The Mortgagee (Lender) will pay out of the set-aside the actual amount of real estate taxes and insurance premiums due each year. The set-aside formula uses current taxes and insurance premiums multiplied by 1.2 to account for increases in taxes and insurance premiums over time.
For additional information see Mortgagee Letter 2014-21 and Mortgagee Letter 2016-10 and the attached revised HECM Financial Assessment and Property Charge Guide, Section 5.4 at https://www.hud.gov/program_offices/administration/hudclips/letters/mortgagee