It is possible. I'm 99% sure I've seen it before here on TB and if my memory doesn't fail me, it was John Kallas @johnk_10 who did that by just making a "pickup" made out of wood that fitted perfectly into the pickup cavity along with matching the wood grain pattern. But I just can't find the thread. Another option is to cut a bigger piece of wood as somebody else suggested. The thing is that you have to refinish the whole body. Here's a video that shows something pretty similar. Hope it helps.
You know what, I've seen that a few years ago and it was Dan's video that triggered my imagination about doing a similar job on my Fender. I wonder if I should send him a pic about getting a neighborhood quote.
