No worries at all. My information comes half and half from personal experience and reading here on Macrumors/other forums. In my past I used to replace batteries for family - that stopped around the iPhone 5 days. An iPhone/iPod/iPad don't run without a battery installed. Power goes through the battery and then to the wall. Most laptops today and in the past, including Macs, will run without a battery installed.
My personal experience: I observe my battery usage with coconutBattery (iMazing on Windows) - my Macbooks will sometimes use 0 cycles in a month because they're plugged in almost constantly but used 8+ hours a day. My iPad/iPhones will cycle through about 10-15 cycles a month even though they're plugged in a lot throughout the month. Leaving my iPhone/iPad plugged in - it still consumes battery cycles whereas my Macbook does not.
Finding sources wasn't super easy but check out some of these:
Macbooks without Battery:
discussions.apple.com
I have a MacBook Pro (2008). It is a secondary computer I rarely use, so it was easy to last that long with it. Such a long lasting service turned me into an adept of Apple quality. I am looking f...
apple.stackexchange.com
iPhone without Battery:
Hi. No, it is not possible to power on without battery. If you can, take it to a repair shop give them to test, and if it works, buy a battery. Or just simply buy a used, but working one, if the phone won't turn on, then the logic board is faulty as well. - iPhone 6
www.ifixit.com
iPad is designed to run with a battery, thus there’s no really easy solution for your need. Not sure if the system requires also a battery presence acknowledgement or it’s sufficient a component bridging, but unless you’re able to microsolder and have the necessary tools is not a very handy... -...
www.ifixit.com
Apple's battery management while plugged in has definitely improved over the years:
https://support.apple.com/en-us/HT208710
I see this as well with coconutBattery - my battery capacity will drop (from design capacity) when plugged in for long periods of time (a lot of my devices spend a long time plugged in). This greatly helps the life of the battery especially with usage like mine where my devices are plugged in a lot.
And you make a GREAT point - the iPad acts like a massive touchpad for the operating system so unless one would have an external bluetooth mouse, it would be counter-intuitive to shut off the screen. Totally agree.
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That the iPad doesn't run completely off wall power and due to the extra resource usage of an external monitor, the battery will be cycled significantly faster when using an external monitor. For my own usage - I'd prefer a clamshell mode where the iPad's screen turns off when I'm using an external mouse/keyboard - like I do with my Macbook Pro - it's clamshelled to a 4k monitor with an external mouse/keyboard.
For some this isn't an issue, just my personal preference.
It is my experience and from what I've read - the iPad will first draw power from the battery, which can be powered by the wall. So the battery is constantly being cycled/used so having to power two screens will result in excessive battery wear.