Could electromigration cause a short circuit in a PCB
It is very unlikely that you would see real electromigration in something as "gigantic" (relatively speaking) as a PC board. We typically speak of electromigration at nearly microscopic dimensions (such as inside an integrated circuit).

OTOH, tin-whiskers are becoming a serious problem with the mandating of lead-free solder. ROHS is creating a whole new class of "planned obsolescence". In fact critical products (medical, aerospace, military, etc.) are exempt from the ROHS lead-free rules specifically because of the tin-whisker problem.