Can my iTunes library be stored on an external HDD and work over multiple computers?

I want to move all of my music and videos over to an external hard drive. If I set the path of my iTunes library to a path on the external drive, will this work okay?
Also I want to be able to get into the library from multiple computers, by changing the path on other computers to the one on the disk drive. Would this work as well?

Would it possibly be worth it to store a copy of iTunes on the external disk itself?