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No, it will not cause an over charge but it does indicate an under charge. It also indicates (with the tools you are using) a 7 tenths of a volt, voltage drop from the battery to the BCM.
The lower voltage shown on the dash gage compared to a measured voltage on the battery terminals is caused by the extra resistance of the wiring and ignition switch contacts, it's unlikely the dash gage will ever give the true exact voltage value of the battery. The alternator regulator circuit doesn't reference the dash gage for charging control, it's independent from that.
