The short answer is no. Not if the current trend of league-wide worsening hitting continues:
Data from Baseball-Reference
The steroid era accounts for the major increase throughout the 1990's, but since 2006 the league-wide batting average has been in a virtual free-fall.
But what about the leaders, the hitters at the top, since we're concerned with anyone capable of breaking .400? For the most part, the trend of decreased average in recent years holds there too:
Data from Baseball-Reference
Using these leaders since 2006, I've attempted to quantify the respective probability each batter could've hit .400, given their batting average at the end of the year:
| Year | Player | BA | Z-Score | P-Value |
| 2014 | Jose Altuve | 0.341 | -3.20 | 0.07% |
| 2013 | Miguel Cabrera | 0.348 | -2.57 | 0.51% |
| 2012 | Buster Posey | 0.336 | -3.12 | 0.09% |
| 2011 | Miguel Cabrera | 0.344 | -2.82 | 0.24% |
| 2010 | Josh Hamilton | 0.359 | -1.94 | 2.60% |
| 2009 | Joe Mauer | 0.365 | -1.66 | 4.84% |
| 2008 | Chipper Jones | 0.364 | -1.57 | 5.87% |
| 2007 | Magglio Ordonez | 0.363 | -1.88 | 3.04% |
| 2006 | Joe Mauer | 0.347 | -2.54 | 0.56% |
In this case, the p-value represents the probability each player could've hit .400, given that they actually hit what's shown above. Therefore the fewer at bats, the more uncertain we are they couldn't actually have hit .400. Thus Chipper Jones's 5.87% is the highest, since he had the fewest at bats of these 9 players.
Just as the league-wide batting average has declined, so have these z-scores and their respective p-values. Over the course of a full season with 500+ ABs, it's virtually impossible (now) to get a hit in 2 of every 5 trips to the plate. That being said, through 257 ABs...
| Year | Player | BA | Z-Score | P-Value |
| 2015 | Paul Goldschmidt | 0.354 | -1.54 | 6.19% |