Yes, you can pick up and use any worker that you have on the board at any time (whether you have run out or not). Didn't check the rules for the specific page as reference - if I find it I'll add to my post.
EDIT: Found the passage on page V of the English rules, highlighted in bold here...
* you don’t have a tradesman on the card
You must ﬁrst hire a tradesman by paying the amount in deniers
indicated in the upper-left part of the card. Place a citizen of
your color on a free space on the card to act as the tradesman.
The citizen must come either from your personal supply (if you don’t
have any, you must hire one for 2 Inﬂuence points - see Inﬂuence),
or from any location on the board (Activity cards, or the principal
buildings, or even expelled citizens lying on a building).
Once the tradesman is hired, the player must put together a
group of dice to activate the Activity card.