Melanotan will kick start your melanocytes into producing melanin. Then when you expose yourself to UV light the melanin changes into a tan. So yes even with a pale pink skin color naturally with the right amount of melanotan and UV exposure your skin will turn brown. See my log with before and after pictures I was extremely pale before I started.
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I also have very pale skin that tends to burn easily. I started using melanotan-free-tan a couple of months ago and have developed a lovely colour. Not too dark, but enough of a tan that it looks as if I've been abroad for a week or two. It's a nasal spray so not as invasive as injecting.