First let's be sure it is a sling and not a pole spear. Pictured is a Hawaiian sling. It shoots a freeshaft, with no lines.
Like Ironhed said, a kill shot is best, but as long as you are shooting a bottom fish, one that will rock up, not swim away, like grouper & snapper, then it very possible to retrieve the fish even if you don't stone it on the first shot.
Of course for this to work you need to have a bottom within your diving range, which is not always the case in Texas, especially on rigs. You also need abnout 15' or more of visibility, hopefully alot more than that.
If rigs are your best dive sites, I'd say you will need a line speargun instead.
I'd look for some spearfishing training. I don't know of any in Texas, but if you ever get to Tampa Bay, look me up.
Capt Chad