Yes, that is how I changed my RED head and plunger/rod assembly, in my hydrant. (you don't want "pressure" on that lower rubber shutoff plunger, when unscrewing the upper RED head/handle = that could damage or tear the rubber plunger, when turning)

Note: I didn't even need to adjust my linkage, when I installed the "new assembly" {note: I had purchased a Complete NEW Y34 assembly, but didn't use the outer hollow pipe and its lower brass unit, (with the drain hole - pee hole}

My old hydrant handle and assembly had been welded before and also had stripped adjustment items for the center rod.

I assume you should be able to "reuse" all your current parts, after your "flushing".