I would expect large majority to have a decent fixed price data packages. However there are people that have slow speeds and/or expensive metered data plans, so I wouldn't get too frisky. Overall bandwidth is usually the bottleneck, so yes.
I am building a chat application(http://tiny.chat) that will use less bandwidth.
Is it worth optimizing reduce as many bytes as possible?
Or the end user doesn't care if there are couple of extra KB used?
A couple KB shouldn't make much of a difference. If your app explodes in popularity, then yes, you should make every effort to optimize.
My question is does the average joe care if app is using less bandwidth or it doesn't matter.
To be honest, for a couple KB's worth of difference, probably not. But I'd assume it'd be good practice to optimize the best you can regardless.