No. Only one person can hold a wish at a time. Reserving locks it, and a second person can't reserve the same gift until the first reservation is cancelled.
That's the whole reason reservations exist: stopping two friends from buying the same thing.
How the lock works
First to reserve wins. Anyone else who tries gets a message saying it's already reserved by someone else. If that person changes their mind and cancels, the wish opens back up and someone else can claim it.
The lock covers that one wish, not the whole wishlist. Everything else stays open to other gift-givers.
A wish has no quantity field, so even if the owner would happily take two of something, it holds a single reservation. Want to give the same kind of thing as someone else? Ask the owner to add a second wish for it.
Good to know
The lock only works on Wishpicks. It stops duplicate reservations here, but it can't stop someone buying the item elsewhere, because the actual purchase happens at the store.
Related
"How does gift reservation work?"
"How to cancel a reservation"