Yes, as long as you format the micro sd card to FAT32. Done it with a 200GB micro sd card I bought from Sandisk and now it shows 999,999 blocks available on my New Nintendo 3DS, no matter how much I put onto it. So you might want to go with something less than 200GB if you want to save money.
It should as long as you format it correctly, however a card like this would more than likely be overkill as i have 128 GB in mine, have practically gone digital (rebought my entire physical library digitally and then went the digital route) and have barely scratched past 60 gigabytes in used storage and still have plenty more to work with.
Plus the 3DS has a 300 games/apps install limitation, so either way this card wouldn't benefit you that much unless your also using it as a video camera or something.
You're better off with a 128 gb, maybe even a 200 gb card.
Yes. 100% it will work. Nintendo only lists up to 32GB as being compatible because only up to 32GB cards come formatted with the FAT32 file system. But you can format up to a 2TB storage device with FAT32. You just need to format it on a PC before use with a program like Win32 Formatter. I have the same model in 128 in my 3DS.