It's grammatically correct but "launched as a new teacher" sounds so strange that I would call it incorrect. It would be understood. We can make it sound fine by using the colocation or stock phrase, "launched on a career." Here are several ways to express your meaning: "Has anyone gotten launched on a new teaching career?" "Has anyone landed their first teaching job?" "Has anyone begun their teaching career?

It's correct, but we don't really say it that way