I chatted with a well regarded engraver a few years ago. He told me what grade surface finish he required to prep the gun (I do not remember what it was) and that due to the nature of how gravers ( the actual tools) work, they will catch and jump off the 'line' intended quite easily. If you have ever tried your hand at freehand checkering on wood you will have an idea. The rougher bead blasted surface would, I think, just have too much to cause grief.
I agree also that to bead blast it after engraving would ruin the careful, and expensive, work. If your engraver (an artist) knows you intended to do that he probably would decline the job.