Would Dumbledore and Severus really expel Harry?

In Harry Potter and the Chamber of Secrets, Harry and Ron fly Arthur's flying car to Hogwarts. They get into severe trouble, and both Dumbledore and Severus tell them that they could be expelled. (Severus being rather nasty about it)

Severus:

Most unfortunately, you are not in my house and the decision to expel you does not rest with me[...]

Dumbledore:

I must warn you that if you do anything like this again, I will have no choice but to expel you.

Would Severus expel Harry, even due to the fact that he told Dumbledore that this was all for Lily?

Would Dumbledore expel Harry, as he is the Boy Who Lived, one of the most important people in their time?

I really doubt that Dumbledore would expel them, however, would Severus?