I would generally recommend the use of a truss rod when exceeding 4 strings or there is a chance you'll experience some bowing of the neck. That said, there are other methods such as building your neck by laminating multiple slabs of wood together and adding a heal to the bottom of the neck where it meets the box. Also there are other factors such as the gauge of string you use. If you use heavier acoustic strings, there will be much greater tension on the neck. If you're going to build using a coiled electric pick-up, you can use light electric strings and decrease the neck tension substantially.
3 or 4 strings, you'll have no problems especially if you use a strong wood such as red oak and glue on a 2nd strip of oak for the fretboard. In fact many of the 3 strings on here were built with poplar, pine, etc.
Once again, though, "There are no rules" Sometimes it's fun to do it your own way and see what happens.
Just my 2 cents.