My initial attempt to settle the question with a google search didn't help as much as I'd hoped:
A search for 'high schooler' revealed approximately 4% of results employing the hyphenated form.
A search for 'middle schooler' revealed a significantly higher rate: 20% of entries employed the hyphenated form. (Including this recent article.)
A search for 'elementary schooler' revealed no use of the hyphenated "elementary-schooler" within the first 100 entries. (I stopped looking after that.) So, effectively, less than 1%.
Based on this search, it would seem that "middle-schooler" is somewhat acceptable and "elementary-schooler" is not acceptable. "High-schooler", however, is unclear.
What I'm needing to decide right now regards the usage of "high-schooler" which I personally prefer to "high schooler". Even though google search trends suggest "high schooler" is used much more frequently, can I get away with using the hyphenated form as a stylistic choice?
My feeling is that if "middle-schooler" is allowed, then "high-schooler" should be just as permissible. After all, someday I might have to type something about a "high high schooler", and I'll wish I had been using the hyphenated form all along.