i think you can learn at home if infact the videos you buy are TEACHING videos, with a CURRICULUM of study, and not just a demonstration of techniques so fast that you cant see them.
some very respected people in the martial arts offer home study courses in practically any martial art, from judo and jujutsu to karate to ninjutsu, and kenpo karate or any other art you wish to learn, testing in these are done via videotape as well, you tape yourself and your partner and send them A COPY of it, you retain the original, and they send you feedback on the same tape you sent them usually addressing any problems they see. although i think learning ONLY with this method MIGHT be better used by an already somewhat experienced martial artist.
and the biggest problem i can see with it is getting THE FEEL of the techniques. and you should also practice with as many people as possible...most of them dont mind if you start a STUDY GROUP for this purpose. and occasionally train with the teachers in person in the form of private lessons or seminars periodically, this will cost money because you will have to travel to them or bring them to you if they are free, so have your partners chip in occasionally and save up.
i have considered some of these courses, but i always ask myself...would you go train with a sensei who earned his certification with a few videotapes?...something to consider if you plan on teaching in the future.
but is it possible...yes! does it really work...yes!
i know people who teach kyusho jutsu (pressure points) on the internet...and have seen demos of the students knocking people out like a pro!...the key is to correct any problems before they progress, everything builds on the foundation (basics)...and the next important thing is to periodically and as often as you can, train with them in person in addition to video training, and TRAIN OFTEN, practice alot.
the people who offer these courses are very respected and sometimes very famous martial artists...and they swear by the video method, and their students via video...the way i see it, if these respected masters, and their organizations feel you are worthy of a rank or certification in their system..then you must be, regardless of how you learned the material.