Cache busting via params

Two questions: Will this effectively break the cache?

Yes. Even Stack Overflow use this method, although I remember that they (with their millions of visitors per day and zillions of different client and proxy versions and configurations) have had some freak edge cases where even this was not enough to break the cache. But the general assumption is that this will work, and is a suitable method to break caching on clients.

Will the param cause the browser to then never cache the response from that url since the param indicates that this is dynamic content?

No. The parameter will not change the caching policy; the caching headers sent by the server still apply, and if it doesn't send any, the browser's defaults.

The param ?v=1.123 indicates a query string, and the browser will therefore think it is a new path from, say, ?v=1.0. Thus causing it to load from file, not from cache. As you want.

And, the browser will assume that the source will stay the same next time you call ?v=1.123 and should cache it with that string. So it will remain cached, however your server is set up, until you move to ?v=1.124 or so on.