Yes, your Mobility Budget is automatically used to pay for car2go rentals in the REACH NOW app. Please make sure that
a) you are logged into the REACH NOW app with the account that the voucher/Mobility Budget was added to.
b) you select a payment method that allows you to use your voucher/Mobility Budget. You adjust this setting yourself in the menu under "Payment data" for your individual payment methods.
c) you do not use the car2go app for the rental.