Sleep mode and network

I was wondering if I put my HTPC computer to sleep or hibernate, is the internet connection still live?
Don't know if live is the right word.

No, both modes shut down every connection active and prevent new ones from being established.

Sleep puts the computer in a low power mode, just keeping RAM active and the CPU consuming minimum energy just for keeping its state, but otherwise not actively executing any programs. Hibernate further powers the whole computer off after saving RAM contents to disk.
In either case, like a powered off computer, network connections will of course not work at all.

Thank you. You answered my question.