I put a Select Number bed in my previous motorhome. The tubes only protrude about 2 inches past the top of the bed. I pushed the mattress up against the headboard and never had a problem with the tubes collapsing or not having enough air flow.
I had closet/cabinets on each side of the bed, and as you suggested, I routed the air lines and pump into the bottom of the closet.
Keep in mind that if you are boondocking without a generator, or don't have an outlet(near the bed)wired to an inverter, you won't be able to adjust the air pressure.
Also, at higher elevations the air pressure would triple the normal setting. Mine never popped, but it worried me a couple of times when I realized how firm the mattress was when I parked for the night.