I would presume that the bulk material in the inside has no need for accuracy, only the very rim. The question is more of whether you can have a coiled material that when uncoiled (deployment) can return to a shape with that level of accuracy. I would think it possible, but I really don't know.
I would forsee a super-precise rim with just a small bit of light shielding on its inside, deployed via uncoiling, and then attached to a much stronger, less precise uncoiled ring to which the bulk shielding material (and stationkeeping ion thrusters) are attached. The attachment between the two would need to provide for vibration and tension isolation (even the slowest adjustments in angle of such a huge, thin shield are going to set in motion relevant vibrations, you've got almost no damping - you want the structural ring to deal with those and not transfer them through to the precision ring). Not to mention that your shield will be acting as a solar sail whether you like it or not (unless you're at L2... but then your craft better be nuclear powered).
Your telescope behind it is going to need to do some real precision stationkeeping (either extreme precision on the whole spacecraft positioning, or merely "good" positioning of the whole spacecraft plus extreme precision adjustment of the optics within) . This means long development times and costs to demonstrate that you can pull it off before you actually build the shield. But I would think that also possible - just very difficult. If they take the latter route they could probably demonstrate that here on Earth, which would be a big cost-saver.