I'm thinking of something like a Chopin waltz (I always keep using this as a benchmark lol). I think that, with a decent amount of effort, it's possible to play a Chopin waltz in a week from memory, with maybe the occasional slip. Would it pass an exam? Possibly, if you're good.
Even measuring what a week of work is for each individual is different. If you simply look at time applied it will be quite various but more importantly if you take effective use of time you will gain more insight into ones ability level. What you might do in one week is a month worth of practice for someone else, so I feel stating the time it takes to learn something is quite all over the place even when we state days, weeks, months etc.
I get your point about sightreading ability, but I think it should be pointed out that there is considerable room for improvement even when it comes to memorizing pieces. And at least for me, memory hasn't had as much to do with sightreading as it has had to do with comprehension, for lack of a better word.
Sight reading develops you in different ways and it specifically improves memorization as the gap between your technical potential expands and reading level closes in on that. At higher levels sight reading and memorization go hand in hand. For example I can learn 100 pieces at once with sight reading skills but this would be rather impossible if one tried to do it via memorization. Memorization does not necessarily rest on being able to play something totally without the sheet music, the definition of memorization expands as your reading skills improve. Yes memorization is also playing pieces totally without the sheets but as your reading skills improve it no longer needs to be exclusively so and you synergize memory and reading to create a hybrid approach.
Of course there are situations where you must memorize (unless you are a sight reading god) but the process you get there (if one wants to develop reading/memorization synergy) requires you read a lot first and wean off the need to read as you purposefully prioritize the muscular memorization. This is of course different for everyone, I am not the best reader in the world so what I might have to memorize to play effectively a better reader could merely read it and play it perfectly without the need to memorize it. This situation is relative to each person, most lower level sight readers will find they have to delegate a lot to muscular memorization if the technical challenges they are reading strain their reading capabilities.
Lower level reading requires that one deals with many easier works and thus it can feel that you still cannot escape memorization to play works which are at your technical potential/interest. However if you put yourself to the absolutely beginner level and try to learn very early music you will find you probably can merely do it all with reading skills and you don't need to memorize like an early beginner might with their very first pieces. So an early beginner might tell you that everything they learn needs to be memorized because its impossible to read and play it immediately without overloading your brain hampering the ability to listen to what sounds you are producing. They need to memorize patterns to be able to play it effectively and reading only allows them to play a passage with difficulties and lack of freedom. This experience is relative and expands all the way up to the higest levels.