If you have no other budwood, then it's worth a shot. Break off the new growth first though. Under good grafting conditions, you could likely get cambium to cambium heal. Then it would just take a little longer for the scion to build up energy again (assuming the rootstock has some energy reserve), resulting in a delayed push. But if there is a choice, you really want to choose something else or wait for the new shoot to harden off before harvesting.
Actually -- you know what you could do: break off the new shoot now and then come back to harvest the scion in a couple of weeks, when it's had a chance to rebuild energy reserves.