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Is Japanese understandable without pitch?

I know that the system to avoid confusion between homophones (regardless of if that was its original purpose) is pitch. The primary standardised Japanese pitch I heard is the Tokyo dialect's form (correct me if I'm wrong). My question is if you can be understood without pitch, and how will it reflect your pronunciation and fluidity. There are many different dialects of Japanese, are they mutually intelligible on the front of pitch? If I don't include the standard pitch of the Tokyo dialect (or the local dialect), will I confuse people, not sound native, or will it be acceptable. If it's acceptable than will it be more like an acceptable mistake or completely fine? If it is absolutely necessary (or of any necessity at all) I suppose I'll put in the extra time needed to learn pitch.

This isn't a duplicate of 'How important is one’s pitch when speaking Japanese?'. The main difference is that question asks of the importance, whereas my question was if I would be seen as foreign, queer, or not fluid or avid.