Self tappers and grp are not a particularly happy combination (in my view). I prefer to through-bolt anything that is likely to get pulled about, though that probably doesn't apply to a halyard bag.
Alternatives to self tappers might be Bighead fasteners bonded on to the grp, or even a strip of hardwood or tufnol bonded on (with Sikaflex), into which you can screw a self tapper.