Does DataCollection allow site transfers between warehouses?

Yes. The function is called Site Transfers in DataCollection GP Mobile.
Site Transfers moves items and quantities from warehouse to warehouse by queuing a Transfer transaction in a SalesPad GP batch in GP. These transactions, along with Inventory Adjustments, must still be posted in GP.

Note: There is also an Inventory Transfer function in SalesPad GP (Modules > Inventory Transfers), which queues transactions to be posted in GP.