From the data I have collected, we can get a feeling for what the B&R percentage would be under the No Conflict Rules (what CJ calls the "break and first shot" rules). We would simply add the run-outs by the non-breaker after a dry or fouled break to the run-outs from the break by the breaker and then divide by the total number of breaks.
This afternoon I went back and calculated this result for the 37 matches (638 games) streamed at the 2012 US Open 9-Ball event. I originally reported the break results for this event here:
http://forums.azbilliards.com/showthread.php?t=293041.
The breaker ran out 145 times in his 638 breaks, for a B&R percentage, as previously reported, of 23%. Since the breaker fouled or broke dry 243 times, he had the first shot after the break 395 times, and his run-out percentage on those 395 opportunities was 37%. The non-breaker ran out after a dry or fouled break 87 times in 243 games, for a non-breaker run-out percentage of 36%. Therefore, the number of run-outs for the player who had the first shot after the break was 145 + 87 = 232. This made for an overall run-out-after-the-break percentage of
36% (232 of 638).
I think this 36% figure is a reasonable first estimate of what the B&R percentage would be under the No Conflict Rules for top players. However, there are a number of reasons why we might not want to generalize from this result. It represents only the streamed matches at one event. Also, importantly, the pros could be expected to break differently under the No Conflict Rules than they did at the U.S. Open. Fouls on the break might be fewer, and I expect the incoming player has a higher run-out percentage after a breaking foul than after a dry break.