Using Arduino as web server and web client at same time

I am designing a new project where I want to POST data from a remote arduino through an ethernet connection. I have this part working. I now want to be able to update the program through the ethernet connection.

From what I found, it looks like I need to set up the Arduino as a web server to do this, and as a web client to actually POST the data.

The remote server will be on a dynamic IP, so I thought of having it send its current IP address each time it sends data. From there, I will be able to access the arduino to update the program.

For now, I am just looking for basic guidance to see if this will work or if there are problems with combining a web server with web client.

I am planning on using a 328 chip, but could bump to 1284p if needed.

Thanks!

Here is an old post with an example. zoomkat's code has a bit of a problem, so read the entire thread.
http://forum.arduino.cc/index.php?topic=319001