You keep the same pool but reshape it into whatever deck you like whenever you like, I think. My one doubt is, does pool integrity work entirely on the honor system, or am I missing something? But mostly this feels like something I'd like to play. I'll have to swing by my LGS on Monday and ask about it.
I've seen some stores in my area run similar leagues. Typically, outside of league days, the card pools are kept in storage at the store until the final day of competition. So there is little risk of people losing or modifying their cardpool outside event time. Of course there's as much opportunity for them modifying their pool in-event as there is in the typical non-competitive sealed or draft event - people inclined to cheat in noncompetitive formats generally get away with it, actual cheat prevention really only takes place at competitive REL.