This might be a stupid question but, with the iron sights sitting so high on the gun, wouldn't the gun always shot low? Or is there something I'm missing.

For it to shoot low the front sight would need to be higher than the rear.

As long as the sight are properly alligned height is of little concern at pistol shooting distances.
At long range higher sights might present a parallax problem.

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Too deep. HK, SIG and others make pistols with extra tall front and rear sights for use with suppressors, and they shoot fine. There is no reason the S&W will not also.

That unfortunate Viking Tactics (VTAC) M&P also has taller sights, and it shoots fine. There is, unfortunately, almost nothing else to commend about that hapless model, but the height of the sights is not a problem. The plethora of dots (4 on the rear, 2 vertical on the front) is, but not the tallness in and of itself.

Yes, for you Kyle Lamb Viking fans, sorry, but the goal of having night sights you can see in the daytime was already solved by both Trijicon and Meprolight by simply putting bright white rings around the trijicon vials.