The hydration process in concrete progresses over a long period of time. Initial hydration during the first few weeks is critical for strength gain. If insufficient water is provided for curing, there will be a delay in the hydration of all the cement in the concrete mix; however, it will eventually occur.
In a concrete mix, about half of the water that is in a typical mix is needed for hydration. The rest of the water is for the convenience of placement. With that in mind, strength gain will occur even if no wet curing is done. The ultimate strength of the concrete will be lower if this occurs; however, it is likely that the design strength will still be met.
The curing process, with wet curing, does a lot more to help the durability of the concrete than to affect the strength, although with wet curing, strength is gained faster and more consistly.
There will be unhydrated cement particles that remain in the concrete after initial curing. If you re-wet the concrete, some of these will hydrate, but they will have little effect on the strength. With hydration though, the durability will improve.