It depends upon how good your eyes are, your sights, the amount of ambient light, the contrast and size of your bullseye, and your skill level (and your sight radius, IF using irons).
If you have very good eyes, good iron sights with a fairly good sight radius, a decent skill level, and a bright day with a high-contrast bull, then getting 1 MOA is quite possible with no magnification; that is to say, with a 1.0 power iron or telescopic sight. For my eyes, which have fairly poor vision, I probably need a minimum of 3 or 4 power to hit 1 MOA at 100 yards - sure would be easier with at least a 6 or 7 power optic at that range. I could do it with a 1 power optical sight with 2 sighting planes easier than I could with iron sights, with 3 vertical planes involved. But even that would take me quite a few tries to do it - a lot of practice - at 1 power.
Of course, you have to have a good rifle and ammo combination, too (i.e. pure mechanical accuracy). 1 MOA is not all that common, despite what reading gun boards might lead you to believe.
The dot on the Eotech pretty much covers a large portion of the center of the target at a yards. I am sure that if i had a 4x-6x clear magnification, those shots could be tightened up quite a bit.
Yes, absolutely, and that there is why my AR15 has a 1.5-6x42mm on it (Sightron S2 to be exact). A 1x dot optic is *fantastic* for close-in fighting, out to 40 or 50 yards. It will also make hits that kill out to 200 yards or more on a man-size target. But it will NOT help you much at all with *precision* hits at 50 yards or more.
My suggestion: Get at least two rifles in 5.56 or 6.8 or 6.5: Set up a shorty carbine with a 1x optic like an Aimpoint or Eotech. Restrict it to CQB only. Don't even try to make small groups with it. It's for run and gun fighting.
Then set up a 2nd, 18-20" bbl rifle on the same platform in the same caliber (for mag compatibility) with a magnified optic - either an ACOG or just any old scope with a 1-4, 1.75-5, 1.5-6, fixed 4, 2-7, fixed 6, or even a 3-9 scope. This is your "all-purpose" and/or "mid-range" fighter/hunter.
Then set up a good bolt gun in a heavy, interdiction configuration for long ranges - something in say, .243 or .25-06 or .260 rem or 6.5x55 or 6.5-284 or .308 or 7mm rem mag or whathaveyou.
With those 3 rifles, you have the bases covered should the proverbial S hit the proverbial F.
If you have to forego ONE of those 3 rifles due to budget constraints, it should be the first one with the 1x optic, because the all-purpose rifle such as I have can handle that role, too, pretty well, espec. with an optic such as I have chosen which dials down to 1.0, 1.5, or 1.75 power. A couple of really good economical scope choices for the "all-purpose / mid-range" fighter are the Leupold VX1, 1-4x20mm ($200) and the Millett DMS 1-4x24mm (also around $200), and the Burris Fullfield II 1.75-5x20mm ($185).