Correct, there are multiple rounds of offers, and yes the person putting said hospital #2 would be competing with others who put that undersubscribed hospital #1 (and that other person who put it #1 would be more likely to get it because it minimises the overall score for that round - this is the entire point of this system).
If you absolutely must get a hospital somewhere in Sydney, for example, as a Cat 2 (for whatever reason) then that would be even more reason to avoid "stacking" and instead putting some safe hospital network first - if your only offer was in (for example) Wollongong, you'd be in a very bad position in regards to whatever it was that you needed to be in Sydney for. Stacking (and not putting a safe preference somewhere high) as a Cat 2 significantly increases your chance of getting something like this, because if the system is unable to give you any of your high preferences then the score it gets for allocating you is going to be high anyway, so it will allocate you somewhere which allows it to free a space for someone else to get a high preference (and thus make the system overall score lower).