Yes, 100%. We only need your minecraft username for the mod to work. You can use any email or password on the website.
I guess your cape doesn't work D: Here's a few things to check:
This mod does NOT work with TLauncher
It's impossible to get a cape everyone can see unless you go to minecon. The only way to get a cape is to use a mod, and only players with the mod will see the cape.