As someone who is learning Ukrainian, which has a similar alphabet, I would strongly recommend that you not skip learning the alphabet. I think you will find that the learning materials, regardless of your end goals, will be limited. Moreover, I find that when I am presented with the Cyrillic form of Ukrainian words together with a phoneticized, latin version, the Cyrillic version is much easier for me to sound out and pronounce correctly.
I would say that the amount of time I had to put into learning the alphabet was very minor in comparison to the time I am needing to learn words, master grammar, etc. It might seem off-putting at first, but I think in the long run you will find that learning the alphabet was well worth it, and ultimately one of the easier aspects of learning the language.
Best of luck!