Cutting LOF can be done even if the borders are pieced, so I think your issue is whether you will have continuous borders or pieced ones, not whether you're cutting LOF or WOF. If EQ says the long pieces will be pieced, it probably means that. It should be very easy for you to check to be sure. Is your fabric as long as the quilt's longest dimension (plus 1/2" for seam allowances)? If so, you can cut your borders in continuous pieces LOF before cutting your blocks. If not, you can't.
I did a test case in EQ7. My quilt was 146.5" square including an 8" border (yeah, huge, I know, but it was just a test) and EQ told me that I needed 3 1/8 yards for the border. 3 1/8 yards is only 112.5", and that would not be enough for one continuous piece in LOF.