I would say there is no "critical mass" referring to total of sign ups to a q&a site. There are too many factors like targeted audience, PR, look and feel of a q&a site, activated options, visits by time period... and so on to determine a "critical mass".
As mentioned before by You, You may compare these two websites. You will see that popanswers has much more visits and users but this site is open for everything.
Preguntaaz in comparison is limited to Mexico related questions on a regional base and is not really a crowdsourcing site. That site is mine by the way.
Typical questions are: What is the phone number of that institution in that village ? or: How can I get in contact with that person from that village ?
Obviously the audience for this kind of question is very small while a question on the popanswers site about Justin Bibers underwear may trigger real crowds to answer or comment.
I wouldnt consider that my site is very successfull, but it is self sustaining.
To get there I added an ask box on one of my successfull regional sites, sending all incoming questions to preguntaaz. Actually I have about 6000 questions but very few people who register.
However, stats show, that half of my visitors are redirected visitors from the regional site where the askbox is and the other half are coming from google and so on. Now, while maintaining an incoming pagerank link from my regional site, I could take off the ask box and preguntaaz would still be self sustaining in terms of incoming visits and new questions, through search engines.
On another site i have just 1000 questions and it is as well selfsustaining.
Back to Your initial question, if You change critical mass into self sustaining and user sign ups into questions on google, than i would answer that a q2a site from 1000 questions on can be self sustaining, completely indipendent of the quantity of sign ups.
I personally think, that having a site growing by itself is all one needs.
The concept, having an askbox on a succsessfull site works well for me and I will go this way, as I could establish with a 5 USD / month investment and some work a self sustaining website and some extra income, which will grow by quantity of quality questions without any further work.