Could a high limit switch cause the furnace blower to run continuously?
Yes.  A bad high limit switch would cause this.  The furnace is trying to purge the heat that it thinks is there. Normally the limit switch will reset when the temperature drops. A bad switch will remain open, so the blower will run continuously. 

This is typically caused by poor air flow through the furnace, which is most often due to infrequent filter changes.   The furnace continually overheats, and eventually the high limit does not reset.

Make sure to change the filter often, and insure that all registers and returns are open and free of obstructions.