Needing regular watering or watering more often does not disqualify plants from succulent'ship, AFAIK, though finding a cut'n'dried, simple definition of succulent isn't as straightforward as one might think. There are many wildly varied definitions out there. Being able to cope with drought seems pretty important to me. Not wilting/transpiring, and the ability to callous over while an attempt is made at new roots, both qualify plants in my opinion, though it IS just my opinion after reading many vastly different definitions of "succulent" from many sources. Depending on the context, the word has different meanings, even in regard to plants.
I think the cuttings are an important indicator. Succulent cuttings kept wet usually rot vs. something like a Coleus that could not survive, even as a cutting, if the soil dried out, and which one would never attempt/allow to callous before propagating as a cutting. Many epiphytes like holiday cacti, Rhipsalis, Epiphyllum break the 'rule' about not being able to cope with drought like many Kalanchoes, Crassulas, Sedums, or Senecios, but are still considered succulents.
Give wax Begonia the same care as Coleus, very little sun, moist soil, it will rot. Put it in a few hours of sun, stop watering so much, big beautiful bodacious plant. It may not fit some textbook definitions, but that's a succulent in my book. I've had the same experience with cane types, dragon & angel wings, rhizomatous Rex types.
My opinion coincides with TX A & M Horticulture department.
http://aggie-horticulture.tamu...
And succulent-plant.com.
http://www.succulent-plant.com...