Did you try it out before asking here? Testing is the best way to find if something works.
There is one big thing you are missing here though - you are putting the form input directly into the mail, without cleaning it first. This leaves open a huge possibility of people injecting nasty code into your form, and sending out spam mails and stuff in your name. You should research injection attacks with email forms a little, and you will find out how to protect against that kind of stuff.
(note: it would have been sent with what you have)