Some statistics I saw not too long ago claimed that the natural bullet spread wasn't so big at those ranges. So yes, at some 200, 300 yards, your rifle can easily hit targets, provided you are good enough.
I have no experience of my own, but yes, the SAW does have a longer barrel. Wiki (don't bite me, I'm not pulling more realiable sources right now, sorry) also claims that the effective range of the M16 rifle is 550 meters, or 600 yards.
With a very good rest modern standard issue assault rifles are easily capable of hitting man sized targets out to 500-700yds if its not too windy. I've seen it first hand, its not a problem for a skilled shooter who knows the bullet drop. And in most cases its not even the accuracy that limits the range to those numbers, its the fact that the bullet slows down from super to subsonic speeds at those ranges, the transition from super to subsonic creates sudden air turbulence which greatly upsets accuracy of the bullet. (I've had this happen numerous times when pushing scoped small caliber (22lr) rifles to their limits, at 75 meters the groups were small as a dime, at 100 meters the groups opened up to palm-size. According to my calculator the transition happens right past 75 meters with most ammo)
That's the ideal situation.
General consensus is that ''battlefield accuracy'' - a pumping heart, adrenaline, low light situations, awkward shooting angles and less than ideal stances in combination with having bullets fly past your head- can be said to be about man sized targets out to 100-150 meters max with a standard issue assault rifle and optical sights like an ACOG, dot or what have you.
That's aimed fire. 99% of the firing that is done on the modern battlefield is barely aimed at all, its mostly cover fire to keep the enemy pinned down until heavy weaponry takes them out. Or a designated marksman/sniper. Its safe to say that 99,99% of the casualties on a modern battlefield are not caused by rifle fire.
That's also a reason why governments are slow and reluctant when it comes to upgrading standard issue assault rifles, it barely makes a difference. They rather invest in better tank armor, precision rifles or intelligent drones than throwing their billions at new rifles that may or may not make the infantry 1% more effective. (unless its a shady deal, hands getting greased and all that)