If you heat treat the belly and then sinew you will most likely be retillering the bow and removing the heat treated belly.
Unless you balance it using side tiller.
Personally, I would tiller out to 24" or so, then heat treat, then sinew nice and even limb to limb, then finish balancing it using the side tiller approach.
Expect to gain a significant amount of draw weight with the heat treat and sinew (depending I the amount applied)
To answer your question though, I think you would be fine to go ahead and work the stave now just as long as you give it several months to dry after sinew