Can Hosts Participate In The Mystery?
It's up to the host. If they prefer, the host can sit out the game and let their guests have all the fun, but in most mystery party games, the host can join in and enjoy the party as much as anyone.
However, when examining the game materials, the host should be sure to not read the solution sheet. Knowing the ending before the game even begins can take a lot of the fun out of the evening.
With very large groups, it may not be practical to have the host participate, as they'll have plenty to do just keeping track up everyone. But for smaller, dinner party size games, the host can certainly play along.