I don't think so. In Ontario, you have a legal profession of 30,000 lawyers, of whom about 22,000 are in practice. Of those, I don't know what the number is, but most lawyers never go to court. What we do in Legal Aid Ontario, of course, is fund lawyers in courts. So we're getting services from only a small fraction of the practice as a whole.
From my own experience, and anecdotally, my sense is that if you are practising criminal law, quite a bit of your practice is likely to be legal aid, with some notable exceptions. But if you're practising family law, for example, you're much more likely to have a mixed practice, where you have some legal aid clients and some cash clients.