Can a home based telescope be used to view galaxies

You can see a lot of things, including galaxies, one of the most popular targets for amateur astronomers (backyard astronomers) is Andromeda M31 which is actually one of the first non solar system objects people try with a decent telescope. You can actually see a lot more than you'd think with a home telescope.
If you want a good set up, get a nice 6 inch reflector telescope (actually around 3-4 feet long). A good inexpensive brand to start off with would be something like Orion. If you ever get interested in the hobby seriously you could spend a years salary on a 10" Astrophysics or Takahashi and stare at the galaxies that ORBIT Andromeda and see quite far out there. The modern high end telescopes for home use are more effecient than telescopes that had to be housed in observatories 100 years ago despite the technology remaining mostly unchanged.

With my 11" SCT, I've looked at around 200+ galaxies. With my friends 18" reflector, I'm able to look at galaxy groups and clusters (collections of galaxies that are gravitationally bound to each other).

Now you can't everything pristinely, most are smudges of light. But they are certainly galaxies.

Here's some that you can look at with the proper equipment -
http://www.astroleague.org/al/obsclubs/a…
http://www.astroleague.org/al/obsclubs/g…
http://www.astroleague.org/content/local…
http://www.astroleague.org/content/local…

Certainly. I have observed hundreds of galaxies with my various telescopes from 7cm to 30 cm aperture.

You can view just a hazy shade of light, nothing more.

No where near powerful enough.