Yes, but Wishpicks hides reservations by default: tap **** reserved at the top of your list, then Show what's reserved.
You can hide them again, but you can't unsee them. Showing covers the whole list, not a single wish, and your other lists stay hidden. Gifters aren't told when you look, but while reservations are showing, the list tells them (see "Will they know it was me who reserved it?").
Steps
Open your list and tap **** reserved in the small line with the wish count, at the top.
In "Show what's reserved?", tap Show what's reserved, or Keep hidden to back out.
Reserved wishes now carry a Reserved chip. Tap Reserved above your wishes to see only those.
Open a reserved wish to see any message the gifter left and, if the list asked them to sign in, their name.
What does **** reserved mean?
It's how many wishes are taken, with the number covered while reservations are hidden. It looks the same whether or not anything's reserved, and wishes marked fulfilled count too. Choosing By reservation in the filters opens the same "Show what's reserved?" window.
How do I hide them again?
Tap Hide next to the count at the top of the list, or Turn it off inside a wish ("You no longer see what's reserved." confirms it). Hiding changes that list's reservation emails too: see "How do I choose which emails I get?".
Can I see who reserved it?
Yes, if they reserved while the list was set to Only signed-in people. While reservations are showing, those wishes say "[name] reserved this.", with the name linked to their profile. The rest say "Someone reserved this.", even if the friend was signed in. A gifter's message shows below, in quotes.
To get names, open the list's Settings (the sliders icon beside the share button, at the top of the list), tap Who can reserve and choose Only signed-in people. New lists start on Anyone, where people reserve without an account and stay anonymous. Switching doesn't name gifts already reserved: each reservation keeps the setting it was made under.
Did they actually buy it? See "How do I mark a wish as received?".
Can the people who help run my list see it?
People with Full Access can once reservations are showing, and can show or hide them too, but Contributors can't in the app. Showing is one setting you share with Full Access: if either of you shows them, you both see them. For Contributors, the app shows no **** reserved, Reserved chips, By reservation filter or gifters' messages.
Tips
Want to know whom to thank? Pick Only signed-in people before you share the list, if you don't mind friends needing an account to reserve.
Someone asking what's still free? Send them the list instead of looking yourself: it shows gifters what's taken (see "How do I reserve a gift?").
If a helper has Full Access, agree who looks, because their peek shows reservations to you too.