Yes, caching of certain items would begin immediately after turning the wiki on, but other types of caching would require visitors.
You might get an influx of visitors that suddenly realize the wiki is back on so they can read that article they wanted to read last week - that also requires a little time to settle down, once everyone feels like they are up-to-date again.
Scheduled tasks would not have occurred since you disabled the wiki. Enabling the wiki would cause the scheduled tasks to play catch-up.
I have found that rebuilding forum styles, plugins, settings, or any cached items like that cause a spike in CPU. This typically happens (sometimes multiple times) when enabling / upgrading the wiki. It would also happen during what may seem like small tweaks to your templates or settings. If you are storing stylesheets (or any other cache) in the file system, updating a large number of files like this at once causes a CPU spike too. If you are using mods like vBOptimise or vBSupercharged, then you have more caches that all need to be updated.