I highly doubt you'll find many controllers doing crazy hours to 'prop up the system' in favor to ASA, more likely for their own back pocket.
There are significant numbers who work overtime to ensure airspace doesn't go TIBA, additionally they come in to ensure their mates aren't stranded alone on a console without assistance. I'd put both of those motivations above the individual financial one or as favour to ASA (which doesn't exist due to the vexatious employment relationship).
Despite what many project (especially ASA managers), most ATCs are highly dedicated and professional; they are unfortunately their own worst enemies (from an industrial point of view). There was some 100,000+ hours of overtime last financial year across the ATC group, spread that out over the operational workforce of around 800 and it's a sh!tload each. The vast majority of overtime was not due to sickleave, it was due to short staffing.
I can see the Press release(s) if there is even a hint of industrial action when negotiations begin early next year... Greedy, huge salaries, generous rostered time off, lots of annual leave etc. etc. Big highlight in difference between O/T worked and TIBA's in 2010 and 2011, sickleave spike... Industrial thuggery... holding a gun to the nation... etc...