Although I don't think that this is possible, I might be wrong since the only Rockbox'ed device I own doesn't have recording capabilities.
If I am correct, that capability could be added easily I think, if your device was able to startup at a certain time (I don't know if it does or not). If it isn't able to turn itself on (and somebody else on the forums with the same player can tell you this), then it's impossible to add this feature, unless you keep the player turned on the whole night.
As I am unsure about my answer, please wait for someone else to reply so you can be sure.
(PS: just curious... what do you want to check in the middle of the night?

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