EAS MUST be set up to automatically interrupt programming. I have it on good authority (an FCC inspector) that any other method violates FCC rules...specifically, the one which states that presidential messages transmitted during an EAS activation must be aired live and immediately.
Almost... The part about the Presidential Level EAS is indeed true. EAS Weekly and Monthly tests are given a window within which you are able to rebroadcast (60 minutes and 15 minutes I believe, respectively).
Yes, Required Monthly Tests (RMT) must be rebroadcast by the participating stations within 15 minutes of receiving them from the area primary station(s).
However, there's currently no obligation for participating stations to rebroadcast Required Weekly Tests (RWT) within a certain time limit of receiving them from the primary station(s). The participating stations must note receipt of a RWT in their operations log (confirming that their EAS receiving equipment is working), but then they are supposed to conduct their own RWT at any time of their choosing at some point within every week (even if they didn't receive one from a primary station, though they should have).
WBMX, the primary FM EAS for the Boston market, sends a RWT every Sunday morning at approximately 3:10 AM.