Yes, as long as you sign up in the same browser where you reserved the gift. Your guest reservations then show up under the new account on their own. Sign up on a different device, or after clearing your cookies, and they won't come with you.
When you reserve while signed out, the gift is held by a temporary guest account tied to your browser. Signing up in that browser links the guest account to your new one, and everything you reserved comes along.
Good to know
This runs on your browser session, not your email. You have to sign up or sign in in the browser that still holds that session. A different device, a private window, or cleared cookies all break the connection.
If it does break, nothing changes for the gift owner. The item stays reserved. You just won't see it listed under your account.
Reserving is a hold, not a purchase, and moving it to your account doesn't change that. You still buy the gift at the store and arrange delivery yourself. See "What's the difference between an editor, a guest, and someone reserving a gift?"
The same rule covers a whole wishlist you built as a guest, not just a single reservation. See "I lost access to a wishlist I made without an account — how do I get it back?"
To be safe, sign up before you switch devices or clear your browser. Once your reservations sit on a real account you can reach them from anywhere.