Yes....... that's why they are adjustable... but to have an effect on draft they must be full length battens. You have not offered us any information about your batten/battens.. For instance, are they full length or partial, what material are they made of -plastic, metal, fiberglass covered foam... are they consistant in thickness or are they "tapered"..
My Nacra 5.2 beach cat has NINE full length, foam core/ glass coverd, tapered battens with quick adjustment end caps. On the beach, at the beginning of a sailing session, the skipper and crew will tilt the boat on it's side with the main hoisted, sight down the sail and quickly make adjustments to the battens based on anticipated wind conditions.
The tapered battens are thinner near the luff than the leech.. if you apply more tension at the stiffer backside the more flexible front end will bend and the draft will not only deepen, it will move forward. Batten adjustment is a big part of Nacra racing. Hobie 16's, on the other hand, have metal, stiff, non tapered battens and do not offer the same dynamic that foam battens do... The Hobie was very popular because it was very simple to sail... no dagger boards, limited sail adjustment and battens that were very difficult to break. Foam battens are not only easy to break, they are damn expensive... at 20 to 40 bucks apiece, and 9 on each sail, you don't see alot of Nacra sailors frolicing in the surf the way Hobie guys would...
So........ like I said... you've already indicated that you understand basic sail trim, and that your single batten may be able to control sail shape. It would make sense that your experimenting with different settings would be more beneficial than trying to find some kind of hard and fast rule. If adjusting the tension on the batten allows you to dial in draft depth and position in that area of the sail, and you can't affect it as well with other controls.. then that's the way to go. With just one adjustable batten it would indicate that you could adjust it while sailing... not something normally done with a beach cat.
Finally, I'd suggest you find a good book on dinghy racing... there are many... that goes into this in some depth. When I campaigned my Laser many years ago the battens were all flat plastic partials whose sole purpose was to support the leech. They were simply slipped into the pocket and left alone.... no one ever talked about batten adjustment. On the beach at Claremont point in Belmont shores.. it was a constant topic of discussion.
