Does the ADC-AC-LP1502-PSE come with a backup power supply?

No. The ADC-AC-LP1502-PSE Door Controller and power supply kit does not come with a backup power supply. If desired, you will need to add your own backup power supply. 

For recommended backup power supplies, see What batteries are recommended for use with the Access Control LP1502 Door Controller (ADC-AC-LP1502)?.