Basically there are two ways you could have an existing 2006 license file. You either have the original license file created for the 2006 product or you have a Subscription to the product and are running a 2009 license file that allows you to continue to run your 2006 product. Since you are moving your license server from corporate to your local office, you might find it difficult to obtain a new license file for your 2006 product depending on the situation because 2006 has been retired.
If your 2006 has never been upgraded, then you can probably receive a new license file. However, if it has been upgraded and is not under Subscription, you won't be able to.
If your 2006 license has been upgraded and is under Subscription, you will need to ask Autodesk for permission to run a legacy license for a retired prior product. Or you can ask that they generate you a Subscription Package license file for 2009. However, if you are under Subscription and when you are ready to update to 2011, you will no longer be able to use your 2006 licenses in this fashion because the 2011 license file will supersede your older file.
What you need to determine is if your 2006 license has been upgraded and if that contract is currently under Subscription. This will help determine your best course of action. In the mean-time, you can create a local server and run 2011 products while your 2006 clients remain pointed to your corporate license manager.