Yes, there is charge sharing and that's the problem.
Imagine a hypothetical situation where we have the charge pump with its output capacitor and the VCO only. Let's say the charge pump output cap is charged to some voltage and the Cm2 is charged to supply with M6 off (we don't care now about M2). When M6 turns on the charge pump output voltage will step up, increasing the VCO frequency.
When the PLL loop is closed we want to have controlled charge or discharge of the charge pump capacitor with a fixed current. However, because we have charge sharing the output voltage steps up a bit and then the current of M2 continues charging it. If the loop doesn't correct it, the VCO frequency will be not what we wanted. But since we have an infinite gain integrator in the loop (i.e. the charge pump) it will have to make the average voltage controlling the VCO such that the average frequency out of the VCO is equal to the ref frequency. To compensate for the charge injection the loop will create a phase offset between the input and VCO frequency in the locked state. This is done by making the UP pulses wider/shorter compared to the DN pulses. However this will result in ripple of the VCO control voltage and respectively spurs in the output frequency spectrum.
From a different perspective - PLL loop is very much like opamp loop, say with unity feedback. Imagine a 2 stage opamp, the first stage is an OTA, loaded with a big cap to ground and then there is the second stage (we don't care here if it is Miller compensated or just the cap to gnd between the two stages is large enough to provide for stability). Now imagine that there is a small current besides the current coming from the 1st stage OTA that also gets dumped into the capacitor. When we close the feedback loop, it will want to make the two inputs of the 1st stage equal i.e. virtual short. But if it does, then the extra current into the capacitor will drift the output of the 1st stage away from the point of virtual short. So, the loop works such that it creates an offset at the input of the opamp that tilts the input diff pair so that it compensates for the extra current and the capacitor is charged to a voltage that provides for the equilibrium in the system.