Yes, it can, though it's difficult to determine unless more than one device is affected after a thunderstorm. Most folks are aware that power surges can enter electronic devices through the power line, but damaging power surges can also enter equipment via network connections (Cable/DSL).
You can help protect your equipment by looking for surge supressors that also have ports to protect Cable/DSL connections. If you want to prevent damage with 100% reliability, you'd need to disconnect all power/network connections when a thunderstorm threatens. Ideally, you'd want to do this before the storm arrives as most lightning strikes occur just ahead of the leading edge of a storm.