The point damage depends on how many inquiries you have already. If you are approved, you can expect a new account to "ding" your score as well, depending on your age of accounts.
These are usually small "dings" that you can recover from quickly, if you don't add anymore inquiries or accounts (let your credit age). However, everyone's profile is different.
Any adverse scoring damage from the addition of a single account is usually overcome within 6 months time. This can vary from profile to profile, but that's a good general time amount that covers most cases.