No, at the moment this would be really hard to do reliably. I have heard a similar request before, though, and it's something I'll think about incorporating. The idea would be to probably have a separate type of routine, for "clock-based" routines.
Right now all routines are relative, so if you want to have it chime on the quarters as you describe, you'd have to wait and start a 15-minute repeating routine at exactly one of the quarters.