Well no, it's literally the employers who move their capital to regimes which allow more exploitative working arrangements to boost their profit margin. That they are so unwilling to accept a reduce share of the company's net income that they will pick up their toys and move to Bangladesh just indicates that we need to be more aggressive against capital mobility.
Would Amazon drivers unionizing cause Amazon to offshore drivers?
If Amazon drivers unionizing would cause Amazon to eliminate drivers, does that suggest unions lack strength, or that unions have strength that Amazon fears?
the whole reason Amazon has it's own drivers is because they can pay them way less. your example would actually represent a big success since ups/dhl/FedEx drivers have much better job security and benefits.