If you measure morning BG you can correlate it with an Hba1c but on a day to day basis it will not correlate well.
I average my morning BG, my feet on the floor BG, over a month and then convert the average to Hba1c. Then I use a running 3 month average of Hba1c as my prediction. This is then checked against whatever lab produced Hba1c I have. There is always an error but it is ball park. I can, because I have some years of records, also apply an average predicted Hba1c to lab Hba1c deviation which narrows the error considerably. From this my prediction is about 1 - 2 mMol out.
The question is is it worth it? I do it because I can and I have a spread sheet set up. My family think, and are probably right, that I am obsessive.
The Hba1c is an, approximately, 3 month average of blood glucose and accounts for all the variations in that period. The finger rick BG is a spot measure. So in reality there should be no actual correlation.