Does AliExpress handle IOSS and VAT for dropshipping in the EU and USA?

It depends on where your agent is (inside or outside EU). if the agent is outside EU that would work , provided that the agent will also use your retail price for customs clearance. One more thing - Ali and the big shipping agents actually do handle reimbursement of VAT for Chinese suppliers , which is another story , but your agent perhaps should be there to handle it.