Yes. While submitting the print book, you will have an option called "Who can buy?". Select "Only Me" in it. The book will then not be visible to public.
After you have submitted your book and it has been approved, log in to you account. Then go to your author dashboard by clicking on your username followed by "Dashboard" on top-right corner. From there go to "My Print Books (POD)". Click on "Store" next to the book you want to buy. This listing is accessible only to you. From there add the book to the cart and complete the purchase as usual.
The steps involved in creating a gift book are exactly like publishing any print book, which you can check out here.
For a gift book you might want to skip editing. You need to format your book and create a cover for it. Then you need to submit it. You can choose to keep it private by selecting "Only Me" under "Who can buy?" option.
If you need help in formatting and designing a cover, you can look at our service.