Rhythm Guitar Posture: Yes, it makes a difference.
Playing acoustic rhythm guitar can be challenging acoustically. Getting the most acoustic potential out of your guitar is one way to make playing a lot easier. Playing an acoustic guitar helps, as does avoiding things like floating pickups that touch and weigh down the top. Suffice it to say that allowing your guitar to resonate as freely as possible is key.
Aside from spending money a nicer guitar, or removing things that dampen the top, or getting better amplification, there is one very simple thing you can do to improve the resonance and projection of your instrument: change your posture.
If you look at photos of Allan Reuss and Freddie Green, both of them have a similar playing position, and that should tell you something! Both cross their left leg over right, and sit the guitar on their left leg, with the guitar angled back, so that the back of the guitar doesn't touch anything. The neck is angled up a bit, too. This position accomplishes a couple things. 1) Such posture allows the top and back of the guitar to resonate freely. 2) Tilting the guitar up helps the player to hear better as well as project a bit further. And 3), the neck position is a bit more comfortable for playing the chords as well. I've looked at many pictures of Freddie, and his legs might have been different depending on the situation and also I think the size of the guitar, but the angle was always there. In his later years, the angle became more and more extreme, until the guitar was almost parallel to the ground.
Here's some photographic evidence:
Freddie Green has the guitar angled out so that the back doesn't touch his body. Charlie has his guitar in a more conventional position, but still angled a bit.
One other thing to note: Allan and Charlie are playing a 17" guitars, and L-5 and ES-250, respectively, whereas Freddie is playing a 19" Stromberg. That's one big guitar!