All you really need to do is look at scores from F-T/R and F-Open to convince yourself that almost no one is shooting at this level of precision. Shooting 1/4 MOA would mean all cleans with mostly X's and it simply ain't happening in the majority of competitions at 600 yd. In LR (1000 yd) comps, no one is realistically shooting even 1 MOA. Some of the better F-Open shooters in regional or national comps are probably close to that as an agg, but I guarantee you they aren't shooting 1/4 MOA at 1000 yd, particularly at the local level.
As an F-T/R shooter, I participate in several matches every month. One is a reduced Palma-type 3 x 15 shot match at 300 yd, another is 3 x 20 at 600 yd, and two LR matches 3 x 20 at 800/900/1000 yd and 3 x 20 at 1000 yd. I have done very well in most of these matches, often winning F-T/R and occasionally F-Class overall. Even in the 300 yd Reduced Palma match, my average is right at 98% and the best score I have shot to date was a 449/450-33X. The rifle I used to shoot that score was a GA Precision Crusader in .308, re-barreled to 27". I can routinely shoot 5-shots groups with this rifle at 100 yds in the 0.4-0.6 MOA range. On rare occasions I might get a group that is a tick better than that, but not very often. So, although the Reduced Palma match uses a target with slightly smaller dimensions (0.45 MOA X-ring and 0.9 MOA 10-ring), why is this rifle that shoots very close to 0.5 MOA at 100 yd in my hands not consistently giving cleans with high X-counts?
It's because of several factors. First and foremost are the wind conditions. Wind, even though it's only a 300 yd match, has a much greater impact on shot placement than it does at 100 yd. As an example, I have another GAP Crusader in .223 that is an absolute laser with FGMM 77 gr commercial ammo. This rifle easily, and I mean easily, shoots 1/4 to 1/3 MOA groups at 100 yd. I know you read a lot of people posting their rifle will shoot 1/2 MOA "all day long". This one really does, and with very little effort on my part. I shot a 439-16X with it in the local 300 yd Reduced Palma match last weekend, which was good enough for 1st in F-T/R and 2nd overall. As an educated guess, that score and the shot patterns of my targets equates to approximately 1.25 MOA at 300 yd from a rifle that shoots well under 0.5 MOA at 100 yd. Why? Because we had very twitchy wind conditions that day, switching rapidly 180 degrees at around 3-5 mph. That not may seem like much, but it's a lot for a 77 gr pill scooting along at only 2730 fps.
Second, you're talking about 15- or 20-shot groups. Comparing the precision of a 3- or 5-shot group (even at 100 yd) to that of a 15- or 20-shot group is like comparing apples and oranges. The group with more shots will almost always be much larger. Just because a rifle can shoot a 1/4 or 1/2 MOA 5-shot group at 100 yd does not guarantee it will do it at 300 yd or 600 yd, or even farther. In some cases the wind might be the culprit, in other cases it could simply be the shooter. In any event, trying to state with any degree of certainty that a rifle needs to shoot "X" MOA in order to be competitive is an exercise in futility. It's all going to depend on the conditions and the shooter. I would be willing to bet that I could take a 1 MOA (at 100 yds) .308 rifle to a 600 yd MR match and post a higher score than some of the competitors with rifles that could easily shoot well under 1 MOA. Does having a very accurate/precise rifle help? Of course it does, but it's not all about the rifle.
If you really want to know how you'll do in a match with a certain setup, just go shoot in the match. Then you'll know. What's more, chances are very good you could then go back a second time and post a better score with the exact same setup. Before my first F-Class match, I had no idea what to expect, so I went with the following thoughts: my intent was to win, my expectation was to come in dead last. I figured anything in between and I'd be GTG. That philosophy worked and I haven't looked back. Don't worry beforehand how you MIGHT do, go out and find out how you ACTUALLY do. Then practice and go out and do better at the next match. I suspect most folks thinking about competing now will be wishing they had gotten started sooner after their first time out. It's a great time.