Would it be fair to say that Christian music is a lyrics-based genre while other genres (rock, blues, country...) are 'music' based? By that I mean, is there a 'sound' to be had playing Christian music like there is an identifiable sound in rock, blues, country, etc.?

There is Christian music that is based upon and played in the style of the above and other genres but, from the point of view of 'playing music', with guitar and other instruments, I don't see Christian music as a separate genre. It's more accurate, I think, to consider Christian music as a sub-genre oif others, e.g, Christian rock, Country Christian, Gospel (blues), etc..

IMO, a better fit would be to present individual song lessons, not a group of separate genre lessons such as those found on GT's Guitar Styles page or in GT's Core Learning System. YMMV.