Yeah, I'd make the most of my last month that way
I'd rather be told, but on some level I could see me not taking advantage of that last month as much as I could from thinking that they might have made a mistake.
There's multiple stories of people who have spent all their wealth from thinking they were going to die... then having to live after that fact.
Depending on the mood and circumstances, it'd either be the laziest or most active month of my life. If it's some catastrophic event world wide I wouldnt have any fun getting rest. But, if it's something linked solely to me like cancer I'd buy a months worth of food and supplies, drive somewhere I can be alone and spend my time trying to figure myself out before I die. Dedicating the entirety of the month on introspection, my character and past/possible choices, missed/taken opportunities and actions/inaction that shaped my perspective. Just as if you wanted to know who made a movie you'd search the credits at the end, I'd just like to go over and see a final review of my life and whether I am/was happy with how I lived it.
Plus, I imagine a new perspective comes out once you're close to dying. People in those situations tend to lose all favor of material possessions and desires, they're forced to see what they truly valued. Just that perspective filter(or lack of) in itself is worth years of thought.