Can you still install Minecraft 2.0 from the 2013 April fools joke?

Solution 1:

Yes it can...

but you will have to download the JAR and JSON files and place them manually in the .minecraft directory, also the download links don't point to the Mojang servers so it can't be guaranteed that the download source is safe.

Download link is in sidebar on wiki page https://minecraft.gamepedia.com/Java_Edition_2.0

Solution 2:

Unfortunately, no.

According to Minecraft Wiki, Minecraft 2.0 is, unlike many of the April Fools' joke versions, not available through the launcher and only distributed to selected people for showcasing.

You can download other April Fools' joke versions like 20w14∞ and 1.RV-Pre1: