Do I have to have more than one case at level one in a multilevel model?

#1
Do I have to have more than one case at level one in a multilevel model with random intercept; and with both intercept and slope? I ask this because Stata allows me to estimate it and I'd like to include as much information as possible.

My study attempts to predict African-American grade promotion probabilities at the school district level (level one), while accounting for state level factors (level two). I'm concerned about the legitimacy of including some states where only school district meets a relatively low threshold number of students (or has only one school district-Hawaii). I'm less concerned about including them in a random intercept model than in a model that also allows for random slopes (which in theory I should do to allow different factors to have different weight between states). So basically, is it ok to include these or not in these situations? Note that my results aren't radically different if they are excluded, however it feels as those I am cherry picking my data.