If I was charged with Fraud under $5000 in Ontario, Canada, went
through the diversion program where my case was subsequently
dropped, and had my fingerprints and photographs destroyed and
removed from the Canadian Police Information Centre (CPIC), would
private firms who do background checks for employers have any access
to any information?  (I went through the diversion program in April
2004, and my fingerprints/photographs are going to be destroyed on
October 13th, 2006. My charges were charged by the York Regional
Police.)

Additionally, if they do have access to this information and provided
it to an accounting firm that has sent me a job offer, does the firm
have the right to decline their offer?  (The firm is one of the Big 4's
in Accounting and I will be working in Toronto, Ontario.)

I doubt the law would force a firm to hire a crook.

I am going to take a guess here and assume that the job offer (if it
is a written offer you can check yourself) is contingent upon the
results of the background check. Therefore they can, in fact, rescind
their job offer if your fraud conviction comes up. In fact, since your
conviction was for fraud (which relates to the job that you are
applying for) you have a greater chance of being rejected if the
criminal background check comes up with it than if you had been
convicted of something unrelated to your future job such
as...burglary.