Naturally, you can begin a statement with the word when: When are you going on vacation? I’ll mail you a postcard once I get there. I was in the shower when the phone rang.
When’re a word, is it?
Theoretically, you can, but it’s not the most effective abbreviation there is. Unlike more common abbreviations like “we’ll” and “there’ll,” the missing letter indicated by the apostrophe still needs to be pronounced when speaking the word out loud, and it only saves one written character when used in writing.
The lack of examples of the “when’re” construction in the Oxford English Corpus supports the idea that it isn’t very helpful.