I want to send serial data from a Simblee 3.3v logic board TX pin to an Arduino Pro Mini 5v RX pin. Can I do this without a logic level shifter since it's only serial data?
Perhaps. Try it and see -- I do this all the time, but not with that particular board.
3.3V is normally recognized as "HIGH" by Arduino pins, but the device probably outputs a somewhat lower voltage, even if running at the full 3.3V.