FYI,
After Ph1 of QL3 COMM RSCH 00120, all the Navy boys and gals were asked if they have completed SQ yet. Most said no, and instead of them going on EWAT they were course-loaded onto SQ.
In short, yes regardless of your element (as it seems) for COMM RSCH you are required to have done and completed SQ. I went Land so I got SQ right about a month into PRETC.