And once again we have a newbie who did not take the time to search for the answer when the answer quite literally is on one of the stickies on page one of this very forum. Look for the definitive guide to wiiu hacking
Yes, yes it does. The Homebrew Launcher can be run on almost all firmwares.
Firmwares 1.0.1-2.1.3 are not compatible, as these firmwares are missing the sndcore2 library which HBL uses for sound.
Firmwares 5.1.1-5.3.1 are not compatible, as there is no public entry-point to run HBL within.
All other firmwares are compatible, including the latest (5.5.1).
As @Marko76 said, a lot of people on these forums would appreciate it if you read the Definitive Guide to Wii U Hacking before asking questions. Thanks.