Probably could but as stated in other posts, it will take more years than it is worth and you will be sacrificing growth better spent towards your graft.

I've recently learned that once a graft takes off, you must cut the above portion of the branch. It can contain a substance that can restrict the growth of any branches below.

o,ok then

simply put, seedling lychees are a pain in the butt. But if you wanna try...=) Yes, I don't see why it can't be done, once the seedling establishes a couple of strong branches what you would do is graft over one of the branch and leave one alone...thereby have a plant that has the known variety and also the seedling. I've done this with my mango. As jay mention, tips of new growth usually contains a hormone that prevents lower parts from branching.