There's really no point. A "self-basting turkey" has been injected with water or broth, fat, and various flavorings. Soaking a turkey in a brine essentially accomplishes the same thing - adding moisture to the bird so that it doesn't dry out while it cooks. Brining leaves out the fat, of course, and is a gentler process, but the goal is largely the same.

Now, how much moisture do you think that turkey of yours can hold? There is a limit, after all.

If you brine a self-basting turkey, some of the brine might flow into the turkey, and some of the "self-basting" liquids might flow out, but you'll be going to a lot of trouble and mess for no effective gain. (Next time, however, buy a fresh turkey and brine it yourself. You'll be pleased with the results.)