Can a person who has Facebook messenger still receive messages in their inbox from people who haven't signed up for FB Messenger?

I looked up a classmate I haven't seen in years, but the "Add Friend" button was not on her page, as she obviously disabled that function. So sent a message to her inbox. Even though he message is clearly there when I go to "messages" (which is now the "FB Messenger" button, thanks to the upgrade), I'm not sure if she will be able to see it. It's kind of confusing, because when I attempted to inbox her on my iPhone, I was forced with the option of signing up for FB Messenger. So I went to my computer instead, where I was able to inbox her without having to sign up for that.

Added (1). Even though THE (not "he") message is clearly there…

Stop… Relax… The answer is no… Stop trying…

Everyone has Facebook Messenger now even if they did not sign up for it or get it when they use the Computer they have Messenger even if they did not download it