I did some testing with my primary gat for Sunday's game, gave me a chance to experiment with my slingster.
I haven't got a proper spare sling attachment on stock end of the gun at the moment, but I threaded it through a built-in loop on my PTS stock, and had it sitting on the outside. And then I tried the 'proper' method, and damn, yes, the gun hangs much tighter to the body (especially when it's basically vertical), it's much easier to get it tucked under the left arm to completely free up the pistol hand too... I'll definitely train myself to stick to it now.
(And I'll order a QD sling attachment for my stock)