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That is what the vendor guarantees the life cycle will be, it may be fine for the next 300 times before it fails to provide adequately low contact resistance. The failures can be due to metal fatigue of the forks that make contact or degradation of the contacts themselves.
I doubt you should EVER connect it when the power is on but regardless, that would not change durability from metal fatigue. Connectors of that type or intended for occasional use, for example linking boards together in an assembly that may never require disconnection or only for rare maintenance purposes. It isn't intended for regular plugging and the figure of 300 will be before it is no longer guaranteed to meet specification, it would probably survive in most applications many more times.
Contact areas surface is specified as "gold flash" (minimal thickness), it's expected to abrade by frequent insertions. That can be a problem for the transmission of low voltage/low current signals. In addition, reduction of contact force can be expected if the contacts are not exactly plugged in centrically and parallelly.
300 should suffice for module connectors and similar applications but can be a problem e.g. for production test adapters. They should have connectors with better specification or interchangeable contact inserts.