Slightly alternative method, instead of copying the whole Steam folder and TF2 stuff.
This method involves creating symbolic links instead of copying the steamapps folder. Basically, you can share a single steamapps folder between all your Steam copies, thus saving you HD space and updating TF2 multiple times.
-Windows Vista or 7
-Ability to follow instructions
Decide your main steamapps folder. Generally it should be the one with most games.
If you want, you can move the steamapps folder somewhere else and rename it (mine is D:\Games\Steam for example)
Remove all the other steamapps folders.
Open cmd.exe as an administrator
Navigate into each Steam folder without steamapps and run the following:
mklink /D steamapps <main steamapps path>
cd C:\Program Files (x86)\Steam
mklink /D steamapps "D:\Games\Steam"
Or if you didn't move steamapps:
mklink /D steamapps "C:\Program Files (x86)\Steam\steamapps"
A shortcut should appear, named steamapps. Double-clicking it should show you the contents of the main steamapps folder.
You're done! Now you can run all the idle accounts while only maintaining a single steamapps folder