I haven’t done it, but I wouldn’t consider doing it either, unless you were vacuuming some type of shell over the blank. Definitely not with a standard 6+6 on top and 6 on bottom glass job. There is a reason stringers are standard issue in a surfboard blank.
I just picked up my first eps 2# stringerless longboard blank (I’ll be adding a stringer, probably three), and man, that is one floppy piece of foam!
Don’t know anything about carbon tape, but I’m having a hard time imagining it could add as much strength as a standard stringer.