Not sure about Gateway on old exploit, but on new one, you can't boot DS games. Neither in Gateway mode or in Classic Mode. (perhaps Classic Mode if booted without Gateway card? Haven't tried that yet). Console just blackscreens and forces you to reboot it.
Either way, you'll be forced to redo an exploit of some kind to get back into emunand. Personally I would find the web exploit easier to do as the DS profile exploit requires you to reinstall it. That's many more steps to go through if you want to play DS games. Web exploit you can just scan a QR code (or have a bookmark if you aren't always at a computer or haven't printed out a QR code of the gateway URL) go into the browser and boot up the exploit. It's not as quick as getting into gateway mode once the DS profile exploit is "installed", but at least you won't have to go through an added layer of stuff to do to get back into emunand everytime you decide you want to play older DS titles.
Something on sysnand checks/fixes the DS Profile anytime the 3DS boots into DS mode. Unless the sysnand encryption is cracked, I don't see Gateway fixing this ever.