Yes.
Refer to the following rules:
Rule 1.5.3.4 When you “Prep a die”, either randomly draw one die from your bag or take a die from the specific play area or card as stated in the ability, and move it to your Prep Area.
Rule 2.3.4 You can only refill an empty bag with all dice from your Used Pile, not from Out of Play, for abilities that state to “draw” dice from your bag.
Also, while not asked, the following rule is germane to your question:
Rule 2.3.12 Searching your bag does not constitute drawing. Therefore, if your bag was empty before searching, you do not get to refill it from the Used Pile to perform the search.
The following link is a good source for these types of questions:
https://wizkids.com/posters/repository/ ... 023%29.pdf