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If I give a character an enhancement that allows me to redeploy units, does that character have to be on the table to use it?

For instance, if I give a Space Marine such an enhancement, can I redeploy units if he's hiding in a Land Raider?

Unless it specifies it can be used from off the table, no.

This kind of rules have no restriction for character basing on bf. Orbital Uplink Reliquary have no restriction. It's gives you rule to redeploy.