Do you pre-ice soft-sided coolers for multi-day use?

I take a large soft cooler (REI Cool Haul 24) for drinks. Bad insulation (compared to rotomolded) and frequent opening mean it’s a losing proposition in some ways. But is there benefit from pre-chilling it with ice overnight like with a rotomolded?

I know having the drinks cold to begin with goes without saying. Except I just said it.