Easy answer to this is yes, but not always. From my experiences, a lot of that will have to do with the estrus cycles. If there is a hot cow in the bunch, there will most likely be a bull around her (likely satellites too at a small distance from the herd).
I think a lot of it has to do with heard size as well. In more open country where herds can be 40+ elk, the odds of a bull being with them is much higher because its just a matter of time before one of those cows is hot, especially that time of year. The part of ID that I hunt is really thick and the largest 'herd' we have seen is around 12 elk which was a lot for one bull to hold on to in that country. The typical band is 4 to 6 cows and we see them all the time with no bull, we just figure there is no cow in estrus and the bulls are making their rounds scent checking other bands of cows. Its funny to watch the tables turn though because the moment one comes into estrus, the valley will erupt into a bugle frenzy with bulls fighting over her.
And mid September is a safe bet to time rut activity right however last year we had stellar elk hunting the last couple days in Aug on the opener, a cow came into early estrus and the bulls were going nuts. I was lucky enough to kill one of them and my buddy was close to killing another however once her cycle was over, the woods became very quiet and we had to return back to a more early season style of calling and hunting which just meant being much less aggressive I guess.