Is it possible to invoke a workflow on an external list programmatically and pass parameters into the workflow? Is there an example using SharePoint 2010?
No, per this MSDN blog, SharePoint doesn't permit association with external lists:
EDIT: I didn't fully answer the question. You can create a site workflow that then looks up external list items, so you could pass in parameters the same way you would to any other workflow.
Not supported with external lists as discussed below. But you can use native lists to simply replicate external data with. In this way you have all list features available, including notifications and workflows in case external data changes.
See here how it works: http://www.youtube.com/watch?v=yEUeLtIA84c
Hope that helps. Regards, Frank