It is viable, but not necessarily the most intuitive way to learn tones. A diacritical mark (above the vowel) offers a visual cue to the tone - a level mark indicates a level tone, a stroke from upper left to lower right indicates a falling tone, etc. The mark serves an important function, that is to help learners recognize the contour of the tone.
The number system, on the other hand, is quite arbitrary. There is no logical reason why the first tone has to be the level tone, and the second rising ... Because of this, it requires the learner to recite all the tones in a certain arbitrary order, and then pick out the one that matches what he sees. To me, it is less direct, and takes longer and more (unnecessary) effort. Imagine trying to learn a language with six or seven tones. You'll find that it's much more time consuming and tedious.
The only pro I can think of for the number system is that it is a lot easier to type :):) But it's probably not a very good reason to opt for it.