Yes! I highly suggest that they do so. Why should the host have to sit out on all the fun? Our games are so easy to host that this is not a problem.
To participate the host can assign characters based on the Guests List instead of reading characters. Do not read the Characters or the Solution to participate in the game.
Also I do not force the Party Hosts to play the roles of the game character hosts. I always think it is best to assign characters by personality, not force someone into a certain role.
If your hosting duties will be heavy, then you might want to play a more secondary character, but there is no reason not to play a character. Reading everything will in no way help the game as our games are driven by the guests themselves. Just follow the step by step instructions in the Host Guide and use your Organizing Labels to have everything ready to hand out when the step by step tells you to. That is ALL the host has to do.