Don't remember getting anything when I still had my Turbobooster Plus powered on without any game. Beside I doubt NEC would throw in a ROM chip for memory manager as that'd add a couple dollars per TB+ made
Theoretically it is possible to have a ROM running inside such expansion that runs when there's no card game but I think only the Super CD addon ever took advantage of this "feature", all CD^2 systems and both AV and/or memory backup never had any added ROM chip.