Leaving the AZA doesn't mean the zoo cannot participate in SSP programs. When Toronto was given the boot over its elephant debacle it participated as a non member participant in all its former ssp programs for two years. Not a single animal was removed due to non member status. It became more difficult to get animals recommended. Some zoos have strict rules about sending its animals to only aza zoos even in defiance of an SSP recommendation. But not all zoos say no. It's definitely harder for zoos who are not members but its not impossible to still be involved. And placing some animals became harder but generally they left even if it took longer.
Now to be fair Toronto was given the boot through no fault of its own (stupid city overstepped) where as Pittsburgh chose to leave. That might have an impact. Hard to say. Participation in SSP programs though is still possible. Plus many other zoos participate as non member participants.