<img width=540 src=http://www.htmills.com/images/LF-bluebirdandnymph.jpg>
I suppose they probably help the sheet around a bit, mostly because of the larger diameter. His regular jib, as you can see, doesn't lap the shroud.
I have four different headsails and use three of them frequently. My sheet is connected thusly (not my pics, but how I do it):
<img width=540 src=http://www.msog.org/how-to/sails/tod_cringle1.jpg>
<img width=540 src=http://www.msog.org/how-to/sails/tod_cringle2.jpg>
<img width=540 src=http://www.msog.org/how-to/sails/tod_cringle3.jpg>
Probably a Lark's Head would hang up the least. Certainly the above method isn't the sleekest, but it does allow for easy sail changes. (one note about that method: on my sheets, the whipping covers stitching that prevents the loop from pulling through and tightening on the toggle. First time I used that method in a stiff breeze I had to cut the whipping to get the sheet off the clew.

The thing I find that makes the biggest difference is to make sure the sheet is all free to run out smoothly without tangles or having to pull around anything more than it has to. Call it pre-tack preparation, if you will.
At one point I had shroud covers but for no particular reason took them off again. I don't use turnbuckle boots since I frequently trailer and that is one more thing to mess with. One possibly good reason for not using boots is that they make it a bit more effort to keep an eye on what's happening there.