In the 308 and 30-06 with a Lee factory crimp die ( No cannelure needed in theory ) I found that a light crimp, or barely any pressure on the downstroke of my Rockchucker, reduced ES and tightened up groups on 125 grain bullet loads but didn't make much difference on the heavier bullets ( 150 and 165).
My theory is that the 125 grain bullets with their short shank benefited from a an increase in neck tension allowing the the ball powder( BL-C(2) ) to ignite more evenly before the bullet leaves the case mouth. I was using magnum primers in these loads and I think the crimp helped prevent them blowing the bullet out of the case before the powder had ignited fully. Too heavy a crimp reduced accuracy though the improvement in ES of the velocity remained the same, the theory here being that the bullets were being deformed excessively by the die and perhaps losing concentricity in the process.
Thinking about it a bit more I then tried a light crimp on some long-seated 155gr Sierra Matchking loads which because of the boat-tail also end up with not much shank in the case neck and found similar results though less pronounced results. Achieving consistency in the crimp with the lee dies was difficult and this was reflected in the ES measured. I would get five rounds within 10 fps ( or the limit of accuracy of the chronograph) and then a round out by 50 fps or more in circumstances where the uncrimped rounds had an ES of consistent 30 fps over something like 50 rounds. The powder used for these loads was RL15
The heavier bullets had long parallel shanks and crimping groves didn't seem to respond measurably to crimping, there were some slightly improvements to ES and grouping but I didn't fire enough rounds to come up with any meaningful statistics.
In the 06 with it's long neck and firing almost exclusively long hunting bullets of 180 grains and up almost no difference was seen at hunting distances, excpet that too heavy a crimp again ruined accuracy. Part of this is that I have a few stable loads with RL17 that produce single figure to low twenties ES variations anyway.
In that rifle I lightly crimp bullets if there is a groove, mainly out of superstition of having the bullets pushed into the case by the battering of repeated recoil in the magazine. The only time I have had bullet setback was with cheap eastern European factory ammo ( MFS if anyone has heard of it ) after empyting a magazine of all but the last round twice on a drive. The bottom bullet was noticeable shorter but fired just fine and went more or less where the rest had gone when I noticed and chambered it.
In short, it depends very much on the specifics of the load. If you have a load you are trying to tune for lower ES via consistent neck tension, it can be worth a try.