Start BOT via API call

Yes.
You can use QueueMessage to send a message to the robot ( or role ) with a command to run a workflow, using a payload similator to this

{
	command: "invoke",
	workflowid: "id-of-openrpa-workflow",
	data: { payload: {"argument1": "value1", "argument2": 42 }
}

from either nodejs, python or c#

or you can start a nodered instance, add a http endpoint and use that to call a robot using the rpa node.
image