The answer really is "it depends".
Sure, moving your hand up as high as possible without interfering will put the axis of the bore lower in your hand and more in line with your arm. Theoretically that will reduce muzzle rise and speed the follow up on the next shot. However that theoretical benefit will usually be over shadowed by all the downsides of a really sucky and inconsistent grip.
There's more to a rapid follow up shot than using a high grip, and that goes double if you actually want to hit something with both the first and second shots - particularly with a DA revolver, where you have a long and comparatively heavy trigger.
If you're one of those folks I see at the range who point a revolver down range and spray bullets all over a B-27 target at 5 yards, then by all means use a high grip and make it your #1 priority. And good luck with that if you ever have to use it for real.
Getting rapid shots on target with sufficient accuracy to have a high probability of scoring the CNS and cardio pulmonary hits you need to actually stop an assailant depends on actually using the sights, having a consistent grip and decent trigger control.
I don't mean lining the sights up like you would in a bullseye match. I mean developing superb consistency in grip over long hours of practice so that the front and rear sights are already aligned with each other as the front sight on the pistol or revolver rises into your line of sight as you are looking at the target. At that point all that is needed is to place the front sight on the spot you want to bleed and finish the press of the trigger. Follow up shots work the same way, releasing the shot as soon as the front blade comes back on target, relying primarily on a consistent grip to ensure adequate sight alignment.
You get to that point over hours of practice and thousands of rounds fired. You start by smoothly and slowly drawing the gun and bringing it to eye level so that that the sights are aligned, then pause to verify the sight alignment before sending the shot down range. Once the sights are coming up pre-aligned, you can pick up the pace and shorten the pause. Eventually the pause just serves as a less than .1 second opportunity to verify the target and the need to shoot.
You'll find your self shooting faster than the guy in the next lane spraying bullets all over the target, and you'll find nearly all your shots are in the 9 and 10 rings with just a couple 8s now and then. If you're shooting an FBI bottle target, you'll find your rounds are all near the center of the bottle.
I can pretty much guarantee you'll never get there using a high grip with a DA revolver.
With a semi-auto pistol, it's less of an issue as a high grip tends to work with a fair number of semi-auto pistols. However, your priority still needs to be on developing a consistent grip, and being able to create that grip starting in the holster. If you're having to compromise that consistent grip, have to shift the pistol in your hand, or feel the pistol shift in your hand, high grip will be counterproductive. Period. If you can make it work with different grips then good for you. If not, screw the high grip as in the larger scheme of things it's just not one of the important issues.
With a DA revolver a high grip can be ridiculously counterproductive.
Look at the two photos below - it's a single hand grip, but I need one hand to hold the camera and it also shows the more critical position in the strong hand.
In the first picture, the grip is low, but the web of the hand meets the grip in exactly the intended spot, and I can create this grip drawing from my holster with 100% consistency. This means that when the revolver rises into my line of sight the sights are already aligned every time I draw, aided to a great degree by the natural point of the revolver with this grip. It also leaves the trigger finger lower with a better angle on the trigger, allowing slightly more precise trigger control with less strain.
With the grip moved as high as possible, short of interfering with the hammer, I can't maintain this grip consistently and it's very hard to create this grip consistently from the holster. Worse, the front blade is too high on the draw and I have to rotate my wrist forward to get the sights on target. That actually interferes with the alignment of my fore arm and slows the follow up under recoil, as well as creating both excessive strain in the arm, and inconsistency from shot to shot. Do it enough and you'll develop what amounts to tennis elbow. If you think you're going to shoot faster in this condition, you're badly mistaken. And don't even think about accuracy.
Now...to be fair, you probably won't develop tennis elbow as the ball of your thumb will be screaming at you long before then as the top for the tang will be slamming into it with each and every shot, and after a fair number of rounds your lower three fingers will be trembling from the effort of trying to prevent the revolver from rotating the pistol upward. News flash - any theoretical benefit you think you gained with the high grip will be offset by the greater tendency for the pistol to rotate in your hand, creating a slower follow up in addition to poor consistency and poor accuracy. The flinch you'll develop with a .357 Mag in a K or J frame sized revolver or a .41 or .44 in an N frame revolver will also render any possibility of accurate bullet placement an impossibility.
Two pieces of advice on DA revolver advice:
1. Before you put much stock in any advice you hear, make sure that person can actually shoot a DA revolver well under real world self defense conditions; and
2. Understand that what is ideal for one person, with their revolver, there grips and their hands, might not work at all well for you.
There's no short cut to finding what works for you, but your number 1 priority needs to be the ability to create and maintain a consistent grip that naturally brings the sights into alignment as you raise the pistol or revolver into your line of sight and place the front blade on the target.
