I'll assume that the VDD is not really intended and that this switch only operates when battery voltage sampling is required. If Q2 also supplies Vdd to the system a different design is needed.
If you drive Qlower gate via a diode D1 from BATADC with a digital high, and add a capacitor C1 to Qlower gate to create a 'stay turned on' time constant with R19, then you can.
Assert BATADC digital high - turns on sampling
Convert BATADC to analog input
Measure battery voltage before falling voltage on C1 starts to affect the reading.
D1 must be silicon, not Schottky to avoid potentially high reverse bias currents in Schottky.
AO3401A is an "entirely OK" part to use - Rdson will probably be around 60 milliOhm. This is insignificant given the value of the resistor divider. BUT that divider MAY be loaded somewhat by the ADC depending on circuit details. Using a sub-10-milliOhm Rdson FET will probably cost no more.
The effect of the 2 x 47k values on precision should be checked (and may have been already).
The AO3400 hs an Vgsth max of about 1.5V which allows lots of headroom when designing the RC turnoff time.