Yes, but the point of rolling for SPD is to see how much power the god decides to give you. It's like you already have a car, just how much gasoline do you have. So you know the spells, you just dont know how often you can use them.
It's more like a car that can go one of two speeds: 10mph or 70mph.
Honestly, rolling crappy spells/day one session is like the GM taking away the wizard's spellbook, except it's a class feature. "Your spells randomly might go away" just isn't fun.