Generally no. The answer used to just he a flat "no". I​​​​​ say "generally" because they are testing (for a second time) an automated bidding system on select flights, but anecdotally its not very prevalent and the recommended bids are usually the same or more expensive (in some cases, way more expensive) than the fare difference. If it's available you will receive an email for CX saying you can bid on an upgrade. Otherwise, no and you should probably count on no.

In most cases unless your flight is part of this bidding test thing, you pay the fare difference. And it gets complicated for the cheaper Y fares since some have high cancellation / change fees .