Mechanically, a Spellbook does two things:
- holds rituals
- holds your wizard encounter and daily powers, in that you have the ability to use a spellbook to swap out your daily load of Wizard powers.
A character multiclassed into Wizard doesn't have ritual casting (if you take it as a separate feat, you just buy/make a ritual book), and they don't have extra powers to "swap out", so the second effect isn't relevant either.
The character might have a book that he's written out rituals and spells in, but mechanically it's not a Spellbook. If that makes any sense. And they don't need to prepare their spells for the day because they don't have a list to pick what to prepare from -- they have what they have.
Since Spellbook is a class feature of Wizard with a mechanical benefit and an "in-fiction" drawback that's only implied, I'd probably let wizards who didn't have access to their spellbook regain their encounters/dailies after an extended rest, just not switch them. That way a wizard without their spellbook doesn't get its benefits, but isn't totally ineffective either.
Heck, I can't even find a definition of the phrase "prepare a spell" in the PHB, so this might even be by RAW. The exact wording is
"After an extended rest, you can prepare a number of daily and utility spells according to what you can cast per day for your level. You can't prepare the same spell twice." That makes me think "preparing a spell" is totally optional, and that if you don't, they follow the usual rules for refreshing encounters and dailies. Doesn't match old versions at all, I know, but so far trying to use 3.x "common sense" with 4e rules doesn't work so I'm trying to avoid it.
