Absolutely! With Oberlo you can automatically send a custom note to your suppliers each time you place an order on AliExpress platform.
Just go to Oberlo > Settings > Suppliers and add a custom note as shown here: http://take.ms/ph5d5. This way, your supplier will be notified to remove invoices or any promotional information in the package.
Try putting there something like:
"I'm dropshipping. Please DO NOT put any invoices, promotions or your brand name logo in the shipments. Please ship as soon as possible for repeat business. Thank you!"
Best of luck!