No, this is impossible, the mode of Vigil can only be changed by manipulation.
In order to change from one mode to another you must switch off your Vigil, switch it on again and enter the setup menu where you can choose the mode you want to use your Vigil in. (Pro, Student or Tandem)
Please remember that no matter the AAD you are using, you must check before each jump if your unit is still on and that nobody implemented an undesired altitude correction which could have the same result as changing the mode. (See example)
While doing this visual check (which requires less than a second on most rigs) it is very easy to READ the mode and/or the eventual implemented altitude correction the AAD has been set in.
This means that any skydiver performing his mandatory pin check properly will automatically know in which mode his Vigil is set.
For example, if you implement a positive altitude correction of 1200 ft on any AAD it will also activate 1200 ft higher (at 2040 ft for Vigil) if your falling speed is still superior to 35 m/s which would be the same as changing Vigil from PRO to TANDEM mode.