If someone were to download a tool like flips to patch rom hacks and Nintendo were to shut down the website hosting the download, could they gather the ips of the downloaders and ban nintendo consoles on their wifi wetworks??
Some might not lead to a ban but plenty could -- if you modify the binary or do a cheat then it could detect that, and if you mod a texture then it could detect that and they do (texture mods can lead to aimbots and visibility hacks if there is any kind of stealth/blend in type feature/mechanic/aspect). Nintendo could also quite easily download the patch/patched game, compare differences and issue a check accordingly.
Even then while cheats might give your game away faster it is also more likely to be the modded firmware that does it these days (anything with an active online service is still getting updates or could plausibly get an update).
I could speculate more on what sorts of hacks they will if not be looking for then likely to fall foul of their checks but it would serve little purpose.
If you had to dump the firmware/keys from your console and used that, and the emulator supported online in some fashion then maybe.
If you mean could nintendo either run a honeypot or get logs from the ROM hacking site and correspond that to their online access logs then possibly but they would not know it was you running the game (shared house, hotel, restaurant, library and all that) or that you used the hack unless you also did the thing above. I have never heard of anything like this happening -- the closest I have really is probably Sony seeking the IP addresses of people that watched a PS3 hacking video some years back.
Nintendo does not generally care about ROM hacks saving that running them usually means third party devices, modded firmwares, pirating software for their devices or potential cheats.
Well, technically yes, but no.
If a website were to give out the IP addresses of the uploaders of ROM hacks, they could ban people based on those addresses, but it could easily lead to false positives, so even if they did care about ROM hacks, they wouldn't do that.
Take fan games. Nintendo loves to take those down, but all the creators get is a DMCA notice. Nintendo doesn't attempt to get their IP addresses and ban their stuff.