I don't think that applies. Unless I misunderstood the GP.
I understood the question as "will I be able to receive messages while the tab isn't open" (offline messages) and "will I be able to read my history on a different device later on" (MAM). Carbons serve a different purpose and sync connected clients (i.e. you chat on your desktop, but your phone receives the same messages as a carbon copy to stay in sync).