Well... If people consider that you are a foreigner from you look or accent for example, it won't be strange.....but for ordinary Persian people..yes it is

You would sound strange, as is the case with just about any other language. But, IMHO, the only way to use colloquial language and not sound strange is to master the formal language first.

In my idea, because you are not a native Persian speaker, it is not very important that you know how to speak Persian in the colloquial form, and if you can just send the meaning of what you say to another Persian persons, it is enough! However it also depends on your purpose for learning Persian.

Yes you will! You should learn colloquial Persian alongside the formal Persian.