Yes, an empty transporter can pick up another empty transporter that has not moved (for example, in the production phase).
The transporter can be unloaded at the start of a subsequent move phase (for example, in the move phase immediately following the production phase in the same turn).
In this way, you could pick up a docked raft in the production phase, then unload it in the river in movement, then move both transporters freely in the move phase.