Of course. And the paper on the insulation is a retarder, not a barrier. Meaning it is permeable which is necessary for our southern humid states.
So you have 3 things going on here.
- The floor covering manufacturer will likely have an underlayment requirement which is different than controlling humidity in the crawl. (however, a humid crawl will effect the recommendation you get from the manufacturer or installer)
- Insulating the building envelope.
- Crawlspace environment/humidity control.
So, Try to pull it all together. Local building code, energy code and floor covering manufacturer will all have a say. (note: I would not install any new flooring until my crawlspace is perfect)