No. Third-party apps such as Charge HQ generally do not prevent Tesla vehicles from entering the low-power sleep mode.
In the past, third-party apps such as Charge HQ could prevent the vehicle from falling asleep, however software changes from Tesla around Dec 2021 appear to have eliminated this issue. It is possible that some older vehicles may still suffer from this issue, especially Model S & X, which is why Charge HQ still has logic to allow vehicles to go to sleep.
This TeslaFi article contains more details on the sleep situation with older vehicles.
Sleep Logic Explained
When the vehicle is parked, Charge HQ continues polling it for 30 minutes.
After 30 minutes, if the vehicle is still parked and not charging, Charge HQ stops polling for 15 minutes to allow the vehicle to fall asleep. During this time, the vehicle is displayed as "attempting sleep" on the home screen, and the vehicle state will not update.
You can cancel the sleep attempt by tapping the help icon next to the "attempting sleep" text on the home screen. This will cause Charge HQ to resume polling.
This logic is enabled for all vehicles and can not be disabled.
