Can a thumb drive be infected with a virus?

Yes. Anything that is connected to your computer that is writable, including a thumb drive, can be infected with a virus or other malware, if it is capable of spreading to alternative drives.

If a flash drive was to become infected with a virus, with most viruses that would mean any time that drive is connected to a computer that computer would become infected with the virus.

If you are running an anti-virus program on your computer if the virus attempted to infect your computer it should be detected. If you are concerned about a thumb drive being infected it can be scanned for viruses like any drive on your computer.