Use AT&T iPhone 5s with bad ESN as iPod Touch? How about Verizon?

I'm planning on purchasing an iPhone 5s with a bad ESN on eBay to use as an iPod Touch, and I'm not sure if I should buy an AT&T or Verizon phone, or if it makes a difference. I have an AT&T and a Verizon SIM card for an iPhone 5s, but I would only use it to activate the phone, then I would remove it to use the phone as just an iPod Touch. I read that you can do this with some iPhones with a bad ESN, but I didn't get a clear answer as to whether it only work with AT&T or Verizon, or if it works on both.

Remember, I don't want the phone to get cellular service/data. I only want to use it with Wi-Fi as an iPod Touch.

A phone with a "bad esn" has been blacklisted, It can't ever be activated on any mobile carrier. You can't get any sim to work in a blacklisted phone.