Yes, it is possible, and you can do this with a script step in an action. Here’s how I’d approach it.
If you use the Draft query function, you can produce a sorted array of drafts from the inbox (order by creation, modified or access date). Then iterate through the array of drafts comparing whichever of the draft’s date properties you use to classify as being a draft “for a given day”. Whenever you get a match to the date part of the property being and your desired date (e.g. today), append the content property of the draft to a variable that at the end of the script you copy to the system clipboard, using the app’s setClipboard function.
That should give you the basic framework. You do need to decide on things like which date property to use, and if you would ever want to allow you to select a date other than today (Drafts’ prompts functionality is what you would need for that). After you have done that it’s then a case of putting together the code.
In case it helps, this acton loops through all drafts and checks the length to identify which are “long’”. There’s a chunk of similarity there in terms of querying for and then processing a set of drafts to find a particular type of match against a draft property.
Hope that helps.