It does allow you to save RAM and might prevent you from hitting swap for a while longer, but it won't save you if your working set is just too large and/or difficult to compress. Apps like web browsers with multiple tabs open might be easier to compress, a game with multiple different assets that are already in a variety of compressed formats, less so.
The Linux Kernel also has a bunch of optimizations (Kernel same-page merging, for example, among others) that do not require compression(although you could argue that same-page merging _is_ a form of compression).
The system is not supposed to 'lock up' when you run out of physical RAM. If it does, something is wrong. It might become slower as pages are flushed to disk but it shouldn't be terrible unless you are really constrained and thrashing. If the Kernel still can't allocate memory, you should expect the OOMKiller to start removing processes. It should not just 'lock up'. Something is wrong.
> which always takes minutes in my experience
It should not take minutes. Should happen really quickly once thresholds are reached and allocations are attempted. What is probably happening is that the system has not run out of memory just yet but it is very close and is busy thrashing the swap. If this is happening frequently you may need to adjust your settings (vm.overcommit, vm.admin_reserve_kbytes, etc). Or even deploy something like EarlyOOM (https://github.com/rfjakob/earlyoom). Or you might just need more RAM, honestly.
I have always found Linux to behave far more gracefully than Windows (OSX is debatable) in low memory conditions, and relatively easy to tune. Windows is a swapping psycho and there's little you can do. OSX mostly does the right thing, until it doesn't.