If you're referring to a watthour meter such as a utility would use a billing meter, the power factor, leading or lagging should not have a direct impact, since the meter is designed to register only real power.
However, overcorrection has two side effects - one is to increase the current flow above what it would be at a unity power factor. This increased current creates some additional losses in the system cabling, although this is a secondary effect and the impact is usually low.
The second issue is that overcorrection can cause your bus voltage to increase. Resistance loads such as strip heaters, electric boilers, etc will draw more power as voltage is increased. However, since these are generally thermostatically-controlled, the impact is generally not significant. Incandescent lighting will also draw more power at higher voltage, but it's not used much anymore, so probably not an issue.