Of cuz you could create chat application using Socket.io with iOS/Android and HTML!
There are 2 ways for you to do it!
i) Implement your own socket communication with Socket.io, (this is diffucult, because you need to write most of the network implementation by yourself!)
Socket.io will interface as stream, that you need to connect from your iOS!
You could refer the iOS dev guide on how to implement the stream!
https://developer.apple.com/library/ios/documentation/NetworkingInternet/Conceptual/NetworkingTopics/Articles/UsingSocketsandSocketStreams.html
There is an active thread that discuss about this too!
iPhone Objective-C socket communication with Socket.IO
ii) Use existing library or wrapper that people make for iOS, you could find the link below!
This library mainly done the networking part, and you just need to implement your app logics!
iOS
https://github.com/pkyeck/socket.IO-objc
Android
https://github.com/nkzawa/socket.io-client.java
It would be good for you to start with the library first and then try to make your own implementation! :))