Yes it is possible to QAYG the BOM.
If you want to QAYG there are several ways of doing it. You could quilt individual blocks or sections. Personally I think the individual blocks are too small to QAYG but, for example, month 1 - A, F and G - would make a nice sized section to quilt as one unit. Alternatively you could break the alphabet into 3 sections - A to J, K to O and T to Z. The main thing you have to remember is that you need to quilt before adding the sashing. The other important thing to know is that you should not trim your blocks to size before quilting as they shrink as you quilt.
So if you are thinking of doing QAYG in smaller sections then the sashing around the outside of A, F and G, for example, only gets added when you are attaching it to either the top or left side border or the B/H block. And, you cannot add the sashing to the front without attaching the sashing to the back too and the sashing on the back will be approximately twice the width of the sashing on the front. Please also be aware that the back of the quilt will be in sections depending on where you joined it on the front. I hope that helps.
I think there might be something useful in the classroom from Sharon Pederson. I seem to recall her doing a demo of adding sashing to an already quilted quilt?