I strongly disagree. Replacing some letters with the others is a written form is not considered as an option in Russian language (except ё/е case). I can see two options for a Russian-speaker to mix "а" and "о" it was either a form or and Internet cacographical dialect called "падонкаффский язык" aka. "олбанский язык" or it was and extremely low educated Russian (like kindergarten spelling level). Also, there are lots of people from ex. Soviet Union countries that know Russian to some extent, but their ability to write and speak in Russian may significantly very depending on the country and educational background. In my opinion, a typical language learner should learn the official spelling and pronunciation first and my explore the variations and deviations later, after mastering the fundamental part. I don't see a reason for a typical learner to deliberately mess their spelling by getting used to incorrect forms. It's far more difficult to fix that later, than to get it right from the beginning. I'm not a amused by Russian spelling either, but in my opinion it's far less difficult than English or French spelling, And I don't know any French course that would offer me a possibility to type words as I hear them (can you name any? 'cause the crazy spelling is my strongest argument against attempting to learn French basics).
P.S. as you progress in Russian, it will get easier for you to check that а/о thing, They are easily confused unless you can find a word where that vowel is stressed. Then its clear which one you should write. For instance:
голова́ (is pronounced like "галава́" with the stress on the last vowel ), but plural form has the stress shifted, i.e. го́ловы, that makes it clear that you have to write о in the first syllable. And to check the middle one, we may use diminutive form голо́вушка. It might be tricky at the beginning, but you'll get used to it.