Is it still possible to install Minecraft 2.0?

Yes, it is possible. The .jar files can still be downloaded and can be found over on the Minecraft Wiki (Working links).

This process should work universally for both Windows and Mac. Linux will also work provided that you have installed the programs needed for .zip archives.

To install them on your client, you will need to open up the .zip archive for whichever version you downloaded and copy the minecraft.jar file.

After that, navigate into your .minecraft folder* and go into the versions directory. Make a new folder there called 2.0 or something similar.

Paste your minecraft.jar into the folder and rename it to the same thing as the folder it's in.

Copy a .json file from one of your other version folders and paste into your new folder. Rename that also to your folder's name.

Open the file in a text editor (Notepad++ does the job well) and edit the "id" line. Change the version value to, you guessed it, your folder's name.

(Note: Depending on which version you copied the JSON from, you may also have to change the "mainClass" value at the bottom to net.minecraft.launchwrapper.Launch.)

Create a new launcher profile.

And hey presto, you can now celebrate April Fools 2013 all over again!

But keep this in mind:

*On Windows, this should be located in %AppData%.minecraft, while on Linux it should be ~/.minecraft. On Mac, it should be /Library/Application Support/minecraft.