Yes, you can.
One way to do it is by creating a command button, then you can choose some quick code snippet from the picker property editor, `MGP_EvalPickerAllSelectButtons` for selecting all nodes in the picker file, while `MGP_EvalPanelAllSelectButtons` is for selecting nodes in that picker panel. Each of mel procedural take mode int value for add/toggle/remove select etc.
If you don't like the mel procedural version, use these direct cmds calls, which are more friendly for Python:
MGPickerView -e -selectPickerButtons $mode; // select all nodes in the whole picker file
MGPickerView -e -selectPanelButtons $mode; // select nodes in the picker panel