Correct, it won't accept the 001E1 (001E1 is the AutoCAD 2013 product key) product code. That is because the software is actually the AutoCAD Design Suite, not AutoCAD and they use 2 different product keys. Also, if you do install it using the AutoCAD Design Suite product code, it may not activate because the serial number is for AutoCAD not AutoCAD Design Suite.
If you want to run it as a trial then yes, install it as a trial for 30 days. If you just want a download of AutoCAD to install with the AutoCAD serial number the the 001E1 product key, then you need to login to the subscription website and download it. If you have a login on the subscription site, then go to: www.autodesk.com/subscriptionlogin otherwise, you may need to wait for the media to arrive.