Unfortunately, no. The FBR certificate, in theory, certifies that you are an Irish citizen by descent. However - the UK authorities will not recognise it, as it is just a a piece of paper to them.
To get a NI number, bank account, job, etc, you will need to apply for an Irish passport, as the UK authorities will recognise an Irish passport as an internationally recognised government-issued identity document. The FBR doesn't have your photo or signature on it, so for practical purposes it will not do.
My FBR backed up with my American Passport has proven to be enough. I already have a bank account and N.I. number within the next 28 days. Going to London on Wednesday to get Passport.