Can overcurrent cause an electrical fire?

Yes, if the overcurrent is not quickly detected by a fuse or circuit breaker, the conductors will heat up from the excessive current, causing the resistance to increase, causing more heat, causing more resistance. This "thermal runaway" continues until the heat gets high enough to damage or destroy the insulation (if any) on the conductors, and deform the conductors to the point of separation. Overheated conductors may possibly reach the ignition temperature of adjacent materials, either with the conductor, sparks from arcing, or from molten insulation, resulting in a Class C fire.