The whole point of a TableAdapter seems to be creating a type safe DataAdapter based on the underlying DB structure / procedures, exposing the DataAdapter as a public property would allow external code to alter things in such a way as to break the TableAdapter (changing the command string, shoving invalid parameters into the commands.parameters collection etc.) and would generally defaeat the point of using a TableAdapter.
If you already have your own data access layer why would you use wizards to generate another one, especially one that doesn't fit with your way of working?
If you need to use DataAdapters directly why not create your own class that exposes them centrally, that would prevent you from needing to use the designers in a 2003 style (they were never that good an idea as they resulted in massive code duplication anyway).