Yes, he raised his average 100 points in just 21 days. As you can imagine, it took alot of work to piece all this data together. But I didn't do it, the fantastic people at Retrosheet did it.
Williams started the year going 21 for 63. As of May 16th his SLG was .571 and his OBP was .425. He actually only pinched hit in each of his first 5 games. So I think no one could have expected what he would do over the next 20 games (let alone the whole season, as I explain below), even though he had just come off two excellent seasons (his first two, at ages 20-21).
From May 17th thru June 6th, he went 40 for 77 with 17 walks, good for a .519 AVG. His SLG was .857 along with a .600 OBP. The .436 was his peak AVG for the year (not counting when it was .500 after his first 4 ABs). But don't be too impressed because Williams actually struck out once in this stretch. And he played 12 of the 20 games in Fenway, where he had a career AVG of .361 while it was .328 on the road (but that is not the reason for the great average since he batted .531 in the 8 road games).
The key Retrosheet link is The 1941 BOS A Regular Season Batting Log for Ted Williams.
Williams also saw a big gain in his offensive winning percentage (OWP) over what he did in his first two years. From ages 20-21, it was .749 (.736 at 20 & .764 at 21). At age 22, it was .908. So it went up .159. I looked at all players who had 400+ PAs at age 22 and 800+ PAs from 20-21 and the top gainers are below. Williams had the 8th biggest gain out of the 78 players who fit the criteria (data from the Lee Sinins Complete Baseball Encyclopedia).
But OWP cannot be higher than 1.000. Williams could only go up by .251. So he gained 63.3% of what was possible (.159/.251 = .633). The next highest in these terms is Powell with 50.1%. So this gives Williams a huge edge. The next table shows the leaders by gain in OPS. Baseball had not seen this kind of age 22 improvement in nearly 50 years.
In the NL in 1894, the year for Kelley, the league OPS jumped .078 over the previous year. For 1893, Davis's year, it jumped .092. In AL in 1941, OPS fell .020 over the previous year (and fell .009 in 1940). So Williams did not even have the help of a general offensive surge.
If we use relative OPS, we can see how incredible his 1941 season was. His OPS relative to the league average from age 20 to 21 was 133 (meaning that his OPS divided by the league average and then times 100 = 133). At age 22 it was 170. I then adjusted every player's OPS to a league average of .750. That gave Williams an OPS of .9975 at ages 20-21. At age 22, he gets a 1.275. So he gained .2775 (round that to .278). Here are the top 10:
Ted Williams 0.278
Boog Powell 0.263
Jimmy Sheckard 0.195
Joe Kelley 0.173
George Davis 0.165
Vic Saier 0.158
Rickey Henderson 0.135
Travis Jackson 0.135
Sherry Magee 0.128
Lou Bierbauer 0.113
Again, until Williams came along, no one had improved quite like this at age 22. No one could have seen his 1941 season or his 100 point gain in batting average in 3 weeks coming.