Bit confused what you are asking. If you don't have internet service, wifi will be useless as it will only work with any local computers/devices you have in the house. You can have wifi without internet, but you won't be able to go to any websites or download anything.
If you are asking if you can configure wifi with your internet connection without a computer, then yes you can, the setup will be in the wifi router and phone, not the computer. So a computer is not needed to setup wifi.
But you need an internet connection to the house to use it.
And you also can't have a smartphone activated without a data plan anyway with any carrier I know of, so if you try to remove the data plan, they won't let you.