In my experience, previewing shows has been a regular occurrence- whether it is in a district I have taught in or one I have worked with more generally. I have seen an urban middle school preview for its feeder elementary schools. In another example, at a rural district of about 1600 students, the high school did a preview performance for the middle school (located a block or so away so the kids could walk over), and the middle school previewed for the two elementary schools (who bussed over.)
Previews serve as rehearsals for our students, a means of building interest in our programs within our schools and across our district, as well as a community point of pride: As you stated, it's a visible means of declaring, "We support the performing arts." Previews also can be an essential piece of learning for students outside our programs. We cultivate audiences and a more general respect and support for the arts by offering these opportunities to all our kids.
I am allowed to do 1 performance during the school day as a promotional tool. I am not allowed to charge for it, and each student who is missing class to perform/tech must have their teachers' permission. The performance is then opened to our feeder schools.
This past year we were allowed to do 2 school day performances. All of the same rules applied, except that the second one was a performance of I Never Saw Another Butterfly and instead of being open to our feeder schools, it was open to our social studies classes. Since it's a fairly short show, the students in the audience just missed 2 class periods. The kids involved in the show always miss the first 4 periods (of a 7 period day).