In my opinion you model a process in order to manage a process. If you want to manage your own activities only, then the answer is no. If you intent to manage customer expectations (which I think you should always do), then the only possible answer is yes.
You can not manage customer expectations if you don't manage the full value chain.
I would say no. Imagine where your process started. Do you capture if the customer is submitting an application or when the application is submitted. I would say the event or trigger starts when the application is received. Please keep in mind you can not model the process of the universe. You are modelling for managing the process of your organization.
Hope this helps.
Gererally i would differ if the interaction with the outside Partner takes place at the beginning or the middle of the process. Additionally i would regard the focus of the model (entire process vs. company internal process).
If the Customer "only" starts the process by e.g. submitting a request, i would possibly ommit the customer from the process and start with the event.
If the process needs more interaction with the outside partner/customer like receiving a confirmation, having documents send to the employee or something lik that i would include him, because he too has vital tasks to contribute to the process. Of course you can model this with events too, but maybe for some reports it might be good to see, where the customer is involved.