You certainly can save your connects as an intern but they are not automatically sent to you. You will lose access to all Microsoft resources on your last day around the end of the business day or slightly earlier. If you return to Microsoft, you will be able to view all of your previous connects, including your intern connects.

If you would like access to your connects and may not be returning to Microsoft or would like to see them in the interim, you can email yourself your connects (email functionality is in the connect) prior to the end of your internship.