Probably. I don't know if every game ask to update but the one I tried asked (If I remember right, it was "Tetris" from the Eshop. Not the Ubisoft one (Tetris Ultimate), the one which is just called "Tetris").
I also don't know if it would update you to the last firmware but anyway, the firmware version was written, so you could easily see which one would be updated. I suppose the 3DS keep a copy of the last firmware version installed somewhere for this purpose). My other 3DS is 9.5 and it offered me to update to 9.5.
jimskeet2002 : You can try, maybe it's only for some games. I just know it happened here for Tetris, and also Smash Bros (Retail carts).
What's you could try is to find a retail cart with download play, to use on your N3DS, and reinstall an emunand on your old 3DS (or to use another SD card). You leave the emunand at 4.x, or 9.0 if your 3DS sysnand is 9.0. If it's 4.x, then you try to update emunand with the download play and see if it work.
Or there is someone who released a method to create a .cia to update emunand manually, so you might be able to update your emunand to 9.0 with that. I think it's Cearp that shared the method if I remember right.