When you say webprogramming do you mean client-side in browser interaction? if so then no and it likely won't for a while if ever as that is mostly in control of the browser vendors, unless you transpile to something like asm.js or something.
As for writing a webserver, if you want you can get down and dirty with windows sockets and do it right now.
If you can do you web programming in C, then Odin is even better for it. The problem is that Odin doesn't have a decent standard library yet (due to the flux in the language) which means you have to do everything from scratch. I've made a little http server demo in Odin before using the Winsock2 API in ~160 lines.
I honestly think that Odin will be great for numerous problem domains including server/web programming.