Yes...IF....they are thick enough. I'd be very careful around newly grafted shoots (snapping them off). Usually you cut off a section maybe 8 inches long (thickness of a pencil or around there) and remove the buds you need... Just remember those buds you place will stay dormant until next spring. Also remember you still have plenty of time...you can keep budding right through August..and probably early Sept where you are. They only take a few weeks to "take"...

Sonny: You are investing your time in a worthwhile project that many have also done. Rather than whacking off the immature new shoots from your grafts in hopes of starting additional new grafts, I think that the better plan would be to acquire quality graftwood from another tree wherein the twigs have already become stiff/wooden on the inside and mature buds are well formed below the leaf stems. I would quickly clip them off, break off the leaves, wrap all but the bottom 2" in stretched Parafilm, and stand them up in a cup with an inch or so of water, where they would stay for a few hours hydrating while in cool shade. I happen to add a few drops of Superthrive in the water, but most do not. The rootstock tree would have been enjoying a l o n g water soaking the day before. If the rootstock tree had new leaves growing now, I would do either bark or cleft grafts. If no new leaves are growing, I would do the cleft grafts. To further protect the sticks from drying up, I also would cover them with a very loose enclosure of white, thin plastic grocery bag plastic for a Sun shield, keeping it unsealed at the bottom.......I am topworking a similar project pear tree for a neighbor this week, since the record-setting 107 degrees yesterday is being replaced with steady, "cool' 93 degrees for the next week. ....Don't let 'em run dry.