In theory yes, it could be damaged by electrostatic discharge (ESD). This could happen if the device is powered off.
In practice it is very unlikely to happen. I would take mild measure to avoid this (don't shuffle on nylon carpets; touch a grounded object before touching the RPi).
Learning about ESD is useful for times when you do need to handle more sensitive devices, or if you ever work in the industry, or to keep instructors happy.
You would normally have a special wrist-strap, with a long lead connected to an Earth bonding point. It is very important that the lead has a safety resistor of at least 1 Mega ohm. This will protect you if you inadvertently touch a live device.
Workspaces have 'conductive mats' which are also connected to ground. Mats come in two forms; normal and high impedance. You'd use high impedance if you're working on a device with a battery in it to prevent the battery discharging through the mat.
Some factories have conductive flooring and workers wear special heel devices.
Other things you should remember are to avoid wearing nylon clothing!