No, but there are ways to do what you are trying to do.
PL/SQL runs with the same OS context and permissions as the Oracle service, so even if you run a procedure as the other windows user, the OS permissions in the PL/SQL will still match the Oracle services. In order to get around this you will have to in some way get the data to where the other user can pick it up or have the other user get the data directly from the database. Here are two ideas, but there are probably many more.
You could create the file in a location that can be reached and then have a job running in the context of the other user that moves it to the protected folder.
Another way would be to have a client application build the file itself logged in as the other user. ik_zelf's answer has an excellent way to do this.