Can I use Brooklet Hill to search through my deck even if my Bench is full?
No. Since your Bench is already full it's public knowledge that Brooklet Hill won't have any effect, so you cannot search your deck.
Source: TPCi Rules Team (2017-06-27)

Relevant cards

Note: All applicable cards may not be listed below.
SM2_120
SMA_SV88
SMA_SV88