Sometimes you have to do a bit of guesswork to figure out exactly what type of driver you're looking at. Here are some clues / deductions:
1) This one takes an input voltage of 0.9 to 4.2V. If it's meant to drive an LED, that's certainly going to be a higher Vf than 0.9V. So you know, at the very least, that this is a BOOST driver.
2) An LED is probably also going to have a Vf that is lower than 4.2V. So it's possible that this driver is also a BUCK. However, the fact that they cap it at 4.2V, instead of giving you the option of going with 8.4V, makes me a little cautious about treating it like a buck driver. Many ICs that are BOOST and BUCK cap the bucking at an input of ~5.5V.
So, thus far, I would only be confident in the fact that it can at the very least BOOST. The next questions that you need to answer are:
A) Whether something that can boost 0.9V to ~3.5V, can also boost from 4V to ~6V. You're not likely to find the answer to that question by any means other than testing. I think there's a decent possibility that it will, but there's also a decent possibility that it won't.
B) Whether this is constant voltage or constant current. The "specs" say that the current is "420mA +/- 50mA". That's a pretty specific figure to be giving if it was a constant voltage driver that had variable current based on a LED's IV curve. So my money would be on constant current (which is good). But, again, you'll want to use a good test load to verify.
