I see some places store their bags of frozen fries right next to the fryer during peak serving periods, Will a thawed French fry cook faster?

Yes, a thawed fry will cook faster, but at some real costs in more oil absorption and in final fry quality.

When frying French fries, do not let them thaw before using.  I recommend that frozen French fries be kept completely frozen before using.  This guarantees that the surface of the potato is sealed during the frying process, resulting in a crispy, high quality fry.  Some operations do thaw potatoes before cooking.  This results in an excess absorption of fat and an undesirable greasy flavor.

This method is called slacking, and while it may speed up the cooking think twice about it being good for the potatoes.