A number of people mash overnight, which is similar to what you're describing:
https://byo.com/stories/item/931-is...mash-overnight-and-just-sparge-in-the-morning
As mentioned in the article, infection is a concern, especially if you don't keep it at a proper hot/cold preservation temperature. Without boiling the wort, it is a breeding ground for wild yeast and especially lactobacillus. This isn't desirable unless you're going for a berliner weisse or other sour beer.
I would just do it all in one day, even if it is possible over two. There are a number of time saving things you can do instead if you're short on time:
-Mash for 30 minutes instead of 60. An hour long mash is the standard but a vast majority of conversion happens in the first 15 minutes.
-Batch sparge
-Immediately heat your runnings when you begin sparging. By the time you're finished sparging your wort will be near boiling.