Yes.
Depending on the motherboard and suspend settings......
Some will physically shut themselves off, while maintaining power to the memory
only... when you power on, it doesn't have to boot up, but it just re-activates
all the hardware and resumes where you left off. This is Suspend-to-RAM.
Other's will continue to run, but just shut down all hard drives and puts the
video into suspend. In this state, moving your mouse or pressing a key on the
keyboard will "wake" up the computer, resuming normal work.
During either method of suspension, network activity is ceased. If you are
connected to the internet, for example, via a dialup networking connection, it
will warn you before entering stand by saying the connection will be closed.
Same thing with a network card.... while in suspend, the computer isn't doing
anything, and so all network activity stops.
If it the Network Interface Card or "NIC" supports Wake-On-Lan (WOL) and is
configured for it, it came with a utility on a disk/cd-rom to remotely activate
the pc via the MAC Address of the network card.