I think you can use BG data to predict HbA1c but you have to be very nerdy to get anything near the lab result.
What you need to do is to record lots of results (several thousand) over several years (so you have several HbA1c results) so you can extract averages (overall 90 day average in the period before the HBA1c or a waking average, again in the 90 day period before the HbA1c) and then correlate them to the HbA1c result. You can use those correlations to predict the HbA1c you will get (together with a statistical error if you are really nerdy) to predict the HbA1c from a current set of results.
I have done this and have had a bit of a laugh with my DSN by predicting the test result when they have been taking blood. Last two, which I have mentioned on the forum, have been very close.
The keys are to correlate your averages with your HabA1c results and to have an awful lot of patience.