If you feel like congratulating your professor, go ahead and do it. He might appreciate it, or in the worst case he will ignore because he has too many emails in his inbox. But I cannot imagine a scenario where the professor would take such a congratulation email negatively.
As with most emails to busy people: keep the email short and to the point. Just one sentence like the one you wrote, though maybe using a more specific term than "your recent achievements":
Congratulations on receiving Grant X[!]
where the use of the exclamation mark [!] depends on where you are and what you have seen your colleagues do in emails (and also on whether you want to use it of course).