Depends on the intensity of the emotions it generates. My own moment of apostasy when it suddenly occurred to me, "Hey, this has gotta be BS" was certainly a personal epiphany, but I wouldn't describe it as ecstatic.
I see your point, Dex. Etymology describes ecstasy as:
"in a frenzy or stupor, fearful, excited," from Old French estaise "ecstasy, rapture," from Late Latin extasis, from Greek ekstasis "entrancement, astonishment; any displacement," in New Testament "a trance," from existanai "displace, put out of place," also "drive out of one's mind" (existanai phrenon), from ek "out" (see
ex-) + histanai "to place, cause to stand," from PIE root *sta- "to stand" (see
stet). Used by 17c. mystical writers for "a state of rapture that stupefied the body while the soul contemplated divine things," which probably helped the meaning shift to "exalted state of good feeling" (1610s).
Online Etymology Dictionary
For your reported event to qualify etymologically as ecstatic, there would have to be "entrancement and displacement" taking place. Even the later definition of "a state of rapture that stupefied the body while the soul contemplated divine things" would not fit your particular moment of epiphany. The meaning shift to "exalted state of good feeling" might fit your experience though.
So perhaps there is such a thing as "an ecstatic secular experience".