Nowadays, I really don't think it makes any difference whatsoever. You are free to use whatever domain you like, so long as it's not somehow offensive or insipid (for instance, if the choice would be considered a curse word or epithet). If there's something potentially offensive, your email could get blocked by a spam server or filter.
Otherwise, though, it really doesn't make a difference. I'm not going to judge a student more or less favorably because they use an email address that isn't a school-based address, or if it's a "vanity address" like the one you've listed.