I'm sure there are players that have memorized the relevant details from most of the (hundreds of ?) spells in Dom3, but I'm not one of them.
The wiki is awesome, and I'm grateful to the guys that maintain it, but as far as I can see it was never meant as a replacement for the manual - it complements the manual more than replaces it.
Ex:
For each spell, the wiki lists path requirement, research level, gems needed to cast, and fatigue. And it has the flavor text, and frequently (but not always) additional info on the spell mechanics that isn't in the manual (this is the stuff that really makes me cherish the wiki - well, in addition to all the other things that make me cherish it).
What the manual gives you that the wiki does not is a bunch of other basic but critical info on each spell: damage, range, precision, AOE, AP?, AN?, contested by MR?, UW vs NUW, etc.
And other than the manual, the wiki is the only place that comes close to gathering all of that info together. The game itself can show you most of this info for most of the spells, but even the game omits this or that (I think?) in it's spell descriptions.
The guys who have been playing the game for a while have internalized a lot of that data on the most commonly cast spells (they already know what situation they want to cast Fireball in, or Thunderstrike, or whathaveyou). But if you were to try to get familiar with the game without having all that data from the manual available, I think that would be rough.
End result, I would estimate that at least 90% of what's in the manual is still relevant / useful to a new player. And since the manual was actually really well written to begin with (despite of the occasional inaccuracy), I think it's totally worth it.
That having been said, if you fall in love with this game there a lot of threads here on the forums that you may want to read up on to learn some of the subtleties / errata that's been uncovered over the years. And some of those are in other places too (Calahan's in-depth study/description of dominion spread mechanics springs to mind).
So, basically what JonBrave said.
