I'm in the industry and can shed a bit of light on this.
There are three types of jobs as testers, or rather 3 types of companies.
1st party (M$ and Sony) and working from home will never happen period. Ever. Never. M$ would fire you on the spot for actually touching the disk. The 360 was locked away You would get a new game every couple of weeks.
Publishers, like EA, Activision etc, also very rare to happen. This is where you would get a new game every month or 3. You would be doing very repetitive stuff compared to 1st party.
Developers like treyarch, Blizzard, Respawn. I work for one, and on a couple of occasions I have been able to work from home, but not on the game, except once. You get new games every couple of years.
I am the manager of the QA team, and I have been able to do it once, so the likely hood that you would get to as any kind of entry position is basically zero.
There are many reasons for this, but the main reason is security. How does the developer know you wont just upload the code to the pirate bay? How, possibly more importantly, does the publisher who is funding this know you wont either. You would be signing an NDA which means they could sue you into oblivion.
Then there is bandwidth. I would say I download upwards of 100GB a day during a work day. Does your BT broadband support that etc?
Of all the jobs I have done in 10 years in the games industry, testing is what I like the most, but it is a job like any other, and can include testing the same level for 2 years. It will not even be a very good game possibly.
Penny arcade made a great comic about it.
http://art.penny-arcade.com/photos/770836278_VG7Cr-L.jpg
This sums up the testing side at 1st party places.
Developers are the way, you may even get your ideas implemented, if you have any.
Also read this.
http://www.becomeagamestester.blogspot.com/