Yes — reserved gifts are hidden from you by default, so the surprise stays safe. You only see which items have been reserved if you turn on the Reveal reservations setting yourself.
How it works
By default, Reveal reservations is off, so you don't see that anyone has reserved anything on your own list. This keeps gifts a surprise. When you turn it on, Wishpicks first warns you with a "Surprise Spoiler Alert!" so you can change your mind — and with it on, reserved items show a Reserved badge so you can see what's already covered.
Steps to keep gifts hidden
Leave Reveal reservations turned off (this is the default — you don't have to do anything).
If you turned it on earlier and want surprises back, turn Reveal reservations off again.
Good to know
Even after you turn on Reveal reservations, whether you see who reserved an item depends on your reservation-privacy setting: the default Anonymous Reservations hides the gifter's identity, while Registered User Reservations shows the signed-in reserver's name.
Reserving a gift isn't the same as buying it. A reservation only marks intent — see the gift-reservation articles for the full picture.
You still get a quiet, in-app Gift reserved notification when someone reserves an item. It names the wishlist, not the specific item or person, so it doesn't spoil the surprise. Depending on your Reservation alerts notification setting, Wishpicks may also email you a periodic reservation summary. Either way, the surprise stays protected — what's reserved stays hidden until you choose to reveal it.
Related
What information is visible to guests?
Who can see my wishlist?