I'm fairly certain you can! I don't know all the programs you can use as it appears the image editor that comes with a Chromebook isn't really usable for pixel art and spriting, but a quick google search showed me that you can download various different apps for free, which you can, in turn, use them for pixeling and spriting!
Here is a link with some of the programs you can use; I'm not familiar with using a Chromebook as I don't use it myself, and I don't use any of these apps myself so I can't help too much. Most of these apps look simple enough, though, and as pixel art doesn't require much use of layering and whatnot, these apps should be sufficient for spriting!
Anyone who has more experience doing digital art on a Chromebook is probably more suited to help, though, but yeah.