I would find it quite annoying to get any of those emails.
When I give you my email, it's not because I actually want to hear from you; it's because you've made it the only — or the least shady — way to sign up. I do not want to hear from you or answer your questions, especially before I've decided that I like your product and care about it.
So any such email I immediately mark as junk, and the fact that you sent it to me will go the "cons" column when evaluating your product vs the competitors.
When I give you my email, it's not because I actually want to hear from you; it's because you've made it the only — or the least shady — way to sign up. I do not want to hear from you or answer your questions, especially before I've decided that I like your product and care about it.
So any such email I immediately mark as junk, and the fact that you sent it to me will go the "cons" column when evaluating your product vs the competitors.