One thing I've been curious about, Did any Popes promise forgiveness of sins or a free path to heaven, by participating in the Crusades?
Sincerely
The Crusade indulgence they received was canonically related to the pilgrimage indulgence.
The Real History of the Crusades
The Crusades were seen as acts of self-sacrifice and love for Christian neighbors. The indulgence received would be similar to a plenary indulgence.
What is an indulgence: