4th & Dragon : Dungeons and Dragons...and stuff

Do characters of other classes who multiclass into wizard gain the benefit of a wizard’s spellbook for the Acolyte and Adept power swap feats?

I’d say no.  The Arcane Initiate [Multiclass Wizard] feat only provides access to one at-will spell as an encounter power and the use of arcane implements (but not arcane implement mastery).

Also, if you take all three power swap feats (novice, acolyte & adept) to Paragon Multiclass with Wizard I would rule that you could double up on your the Paragon dailies and utilities only.  As you didn’t get the Spellbook feature until after you took the feats and you can’t retrain powers across classes (PHB pg 28) it doesn’t make sense to allow use of the feature on the powers involved with those feats.

I might not have understood your question exactly, but I think I did!

No because you lack the spellbook class feature.

I was planning to make an extra feat to gain it, because it is not really too unbalancing to get that with a feat. Sort of like an expanded spellbook, but for classes that multi into wizard.

Alright, if a strict RAW says no, should a character that multiclasses into wizard and takes Acolyte or Adept Power gain that ability?  Preparing spells, after all, is a defining feature of a wizard and it would be kind of strange for a character who is multi-ing as a wizard to not prepare spells.

Also, I’ll point out that a character who takes Arcane Initiate and has Wis 13 (or higher) already qualifies for Expanded Spellbook.  However, since only wizards prepare spells, it’s of dubious value since it will run into the same issue that sparked my original question.

Even RAI does not say that you should gain features of another class simply via implied means.
What I mean is, that you should not assume that if a wizard casts spells AND wizard uses a spellbook -> characters who gain wizard spells ALSO gain the spellbook feature.

I would just make a feat similar to the spellbook feat (or change its wording) so that the class feature is available at a cost of a feat if the character wants to have it.