Well, how SmashStack runs is by pretty much running whatever Boot.elf is in the root of the SD card.
What SmashStack does for Brawl Hacking is by causing the Boot.elf to be Gecko OS or Riivolution, which allows the hacks to run but installs nothing.
If you're asking if you can run Brawl hacks on a Wii without installing anything, yes, that's very possible. My and my friends run Project M off our school's unmodded Wii all the time using SmashStack.
If you want to actually install the Homebrew Channel, its as simple as changing the boot.elf to be that of the Homebrew Channel installer.
Did that answer your questions? I don't know if I understood them fully.
Not really. He wants Homebrew and hacked Brawl. I want to know if it's possible to have the SmashStack files and hacked Brawl files together on the same SD card and have everything work. Meaning the hacked Brawl files will be on the SD card while Homebrew is installed using SmashStack and hacked Brawl will run while the SmashStack files are still on the SD card. It would be so much easier if I only had to give him one of my SD cards since anything less than 4GB is kind of a pain to find nowadays.