I have an M&P that is similar to the one shown, but mine came with the free float, full railed handguard on it. It also came with what appear to be Troy BUIS on it. I also have an Aimpoint ML2 mounted on a LaRue M68 CCO cantilever mount. The BUIS do cowitness in the lower third of the tube.
I also have an Armalite M14A4(C) with GG&G BUIS and an Aimpoint M2 on one of GG&G's cantilever mounts. The BUIS cowitness more towards the center with that set up, and I actually prefer that more, as everything is regulated to the sights instead of the dot.
Either way, I prefer the irons down, and it offers a cleaner view, with no clutter. The sights can be up in a couple of seconds if need be.
Other than being annoying, it really doenst matter if anything is in the way, or if the front cover is closed, as long as you shoot with both eyes open.
Of the two, I do think the GG&G sights are the better sights. They are more solid and robust, and have little if any movement of the sight itself when up. The Troy's have a lot more play in them and I dont seem to shoot as well with them either.
I dont believe the specific model of GG&G front sight I have will work on the M&P though (height wise). The front rail on my Armalite appears to be lower than the rear rail. The M&P rails coincide, or, at least mine do, so I dont think they'd line up. This may be an issue with others too, so you may want to verify things before you buy.
This is off-topic, but please remember not to shoot 5.56mm out of that thing. That's a .223 Rem barrel, not a 5.56mm. It will cause problems.
Mine is marked 5.56 NATO 1/9.
I've shoot both out of both, and never had any issue. Same with .308/7.62.