I am going to attempt to answer your question the best I can. When setting yahoo mail up in outlook what happens is this. The Outlook client downloads mail from server. Depending on configuration you have two options.
1. Download email and leave a copy on server(Fills up fast and stops mail from being received when full)
2.Download email and do not leave a copy on server.
In regards to the client and email server syncing that is more or less what occurs when you login to Outlook to check your mail. I would not recommend managing email from multiple clients. Ex web page and Outlook.
Pick a solution that works for you and stick with it. This will work best.
If you have any other questions I am here don't hesitate to contact me.