I think you can. But what's the point?

I would guess that's how they teach Mandarin to native speakers of other Chinese "dialects." I don't believe they bothered to invent pinyin just so they could romanize place names.

Ha ha this question is so cute....But language learning not only include speaking but also writing.Don't you think so？

yes, it's possible

If you learn Japanese, that could be read and written only in letter similar Pinyin. But Chinese materials including books , magazines or websites are mostly printed only in characters without Pinyin. How to get used to it or make sure you understand what they are actually. I think it is hard in the beginning of learning, but try to keep on it and that will be interesting！ Good luck!