If you mean to use the L129 - Probably not, I highly doubt any TA Bn's has any to actually train with. If mobilising the Bn you're going with can put you on one.
If you mean in general... It's down to the TA Battalion if they want to run one internally, mine does but obviously not with the L129. We were lucky to have some ex-regular Sniper SNCOs and one or two PSIs with the same experience. Does it add to capability? Not really in our peacetime weekend warrior-ing. We can't afford the man power on a Bn Weekend to let a load of blokes that did an internal course to run around pretending to snipe so the 'Sharpshooters' just find themselves with a crap certificate and still bodding it in a Platoon.
From what i know there is no current course to use the sharpshooter weapon, just like any other weapom just a WHT and ACMT. None of the blokes i know who've used it went on some special course. However i may be wrong.