Yes, your customers can schedule to send gift voucher in future day. It's a really nifty feature we've built in to our checkout. They can choose any day in the future, along with a time to send the gift voucher to recipient.
Note that this feature only applies to digital gift vouchers, so if you have our postal feature turned on, it won't apply to those orders.
From VaocherApp Dashboard, you will be able to see the scheduled date & time and also cancel the schedule if you want: