The technology is there to do this. And the funny thing is that unless you have the correct (read as actual) plates and specific screening machine utilized by the watch companies you are likely to get better results this way. The watchmakers use dedicated screening machines and permanent micro-tolerance jigs which are built to very tight specs themselves. Because of these facts screening almost never ends up in truly accurate numbers or proper date alignment within the box. Look at all the travails Finepics and Lello have undergone. And, let me be clear, that I am not criticizing their work. I am sure it will be very good when complete.
But even with the date overlay alternative critical elements of getting it right include utilizing proper thickness non-fade printing material, readily usable adhesion system for proper alignment, appropriate quality and form of printing and ink and very precise cutting. You would be surprised how complex it becomes. But you can get it perfect. And the best part is that once it is perfected it is very easy to make datewheels for a number of different brands.