Fairly quick, depending of course on the weight of the page(s) and how many archive methods you enable (I have several turned off because they are redundant for my purposes). The "adding to archive" interstitial still tends to time out which is a little annoying, but the actual archive process is backgrounded so it doesn't matter.

The recommended install includes a search engine that works well, aside from a few false positives due to being fuzzy search. I don't have much in it yet so I can't say what the performance is like once you reach e.g. thousands of pages, but I imagine it would still perform well except maybe for mass operations like rebuilding the entire index.