Welcome to reloading and thanks for asking our advice
Yes, absolutely.
When you understand the steps of reloading, you can vary your approach any number of ways. As long as you get all the steps done. For some it is important which comes first and for some it does not matter.
One way: You can remove the depriming core of the sizing die if you want to deprime and reprime before doing anything else. (Use a universal depriming die, which does not size the case, then reprime with a hand tool.) Do a thousand cases and store them. Then, when you want to load, size (without depriming) and all the rest of the steps on the primed cases.
That is not the only way. Plan your process flow like any planner would lay out a factory production line. Examine various product flows and choose the one that suits you best.
I considered priming by hand, but the time penalty discourages me. Besides, I have not found that the "feel" is any better with my various hand priming tools (two hand primers, RCBS and Lee and one bench primer, RCBS) than my presses (RCBS Rock Chucker and Lee Classic Turret, Pro-1000 and Challenger). All I have to do is get used to how it feels on the press.
The RockChucker has plenty of leverage, so I use the lever gently with just fingers and feel the primer bottom out very easily - better in fact than I can feel it through the Lee hand primer's linkage. With the other presses, I have adjusted the operating lever so that it is close to the press frame. As the primer hits bottom, I can feel the lever's movement in relation to the frame by wrapping my hand around both. It is very easy to feel when the primer hits bottom.
Good luck,
Lost Sheep