My very first machine, made from bits I had laying around to see if I was serious about building a cnc machine, used something like that. A pair of thrust bearings either side of a plate to resist the axial loads. The stepper was then connected to the ballscrew using a very stiff and tight fitting piece of rubber tube to act as an alignment coupling. Something off a car engine cooling circuit ?

The coupling worked fine for many months, but the thrust bearings became noisy and needed regular adjustment. I think this is because they were held there by a locking collar and did not apply a preload. Your picture has a preload nut so this will be better. By all means try it as it is much better than using the stepper bearings.