Can i download apps with no celluar service?

I have an old iPhone 3gs and i want to download some apps onto it
I found that i can still logon to my game center account and i can still access the App store.
This phone has no service of any kind. Can i still download some free apps without charge?

Added (1). Being more details i want to download textPlus. Can i do this without charge?
and is Wi-Fi free?

Yes if you can get to Wi-Fi.

Yes, as long as you have a Wi-Fi connection and a iTunes account

Yeh you can
by using Wi-Fi
Wi-Fi got nothing to do with the carrier
if you have a laptop or tablet that has Internet in your home than you got Wi-Fi
hope I helped.
if you need help or got any question you can email me at spieleranswers@outlook.com