After completing a mission, two agents had personal disruptor shields on, but they did not recharge to 100% once back to the Geoscape. They also did not recharge after hours had gone by.

When back at base, if the PDS is dropped into the base inventory, it can immediately be placed back onto the agent fully charged.
Rechargeable weapons can be added to this list as well. In build OpenApoc-v0.1-606-gd53c36dc with the weapons mod, I saw laser pistols did not recharge after I finished a mission, but they would recharge as soon as I entered one. I have not tested other weapons but would assume they would follow this pattern.
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When back at base, if the PDS is dropped into the base inventory, it can immediately be placed back onto the agent fully charged.