My opinion is yes. The state of each character is determined at the start of the round. So at the very start of that first round, Stealthy is UNseen, meaning if her card is revealed in the first round, she CAN escape during that turn.
Except for the game setup specifically tells you otherwise:
"The Witness/No Witness card is placed next
to the board, with the Witness side up for
the first turn"
The Witness is face up on the first turn, thus Jack can not escape, regardless of his character.