Can the network take my drivers during service?
No. A courier on shift with you is not offered network jobs at all. Your shift always comes first. Between shifts, they can take freelance work from the network if they want it. Your drivers stay yours, and they can earn more in their idle hours without costing you anything.
In more detail
This is the first question most restaurant owners ask, and the answer is enforced by the software rather than by policy. While a courier is on shift with you, the network does not offer them anything. There is no decision for them to make and no temptation to manage.
The reason it works in your favour: a driver who can earn between your shifts is a driver who stays available for your shifts. Retention is the hardest part of running your own delivery, and this is the part of the arrangement that helps with it.