Can position data be modified in onUpdate while gps is on?

The value g is a position object that your application owns. It is not shared by the system in any way. You are free to modify it to your hearts content.

As this code is, you are getting the current position, overwriting it, and then throwing that away. What you want to do is capture the current position in a variable, and modify that variable from your InputDelegate and display the result in the View. Something like this.

import Position;
import WatchUi;

class MapModel
{
    hidden var mLatitude as Float;
    hidden var mLongitude as Float;
    
    function initialize(position as Position.Location) {
        var degrees = position.toDegrees();
        setPosition(degrees[0], degrees[1]);
    }
    
    function getLatitude() as Float {
        return mLatitude;
    }

    function getLongitude() as Float {
        return mLongitude;
    }

    function setPosition(lat as Float, lon as Float) as Void {
        mLatitude = lat;
        mLongitude = lon;
    }
}

class MapDelegate extends WatchUi.BehaviorDelegate {

    hidden var mMapModel as MapModel;
    hidden var mHeight as Number;
    hidden var mWidth as Number;
    
    function initialize(mapModel as MapModel, screenWidth as Number, screenHeight as Number) {
        BehaviorDelegate.initialize();
        mMapModel = mapModel;
        mHeight = screenHeight;
        mWidth = screenWidth;
    }
    
    function onTap(evt as ClickEvent) {
        var xOffset = mScreenWidth / 10;
        var yOffset = mScreenHeight / 10;
        
        var leftEdge = xOffset;
        var rightEdge = mScreenWidth - xOffset;
        
        var topEdge = yOffset;
        var bottomEdge = mScreenHeight - yOffset;
        
        var posX = mModel.getLongitude();
        var posY = mModel.getLatitude();

        var coords = evt.getCoordinates();
        if (coords.x < leftEdge) {
            posX -= 1.0;
        } else if (coords.x > rightEdge) {
            posX += 1.0;
        }
        
        if (coords.y < topEdge) {
            posY -= 1.0;
        } else if (coords.y > bottomEdge) {
            posY += 1.0;
        }
        
        mModel.setPosition(posY, posX);
        WatchUi.requestUpdate();
        
        return true;
    }
}

class MapView extends WatchUi.MapView {

    hidden var mModel as MapModel;
    
    function initialize(mapModel as MapModel) {
        MapView.initialize();
        mMapModel = mapModel;
    }
    
    function onUpdate(dc) {
        var lat = mMapModel.getLatitude();
        var lon = mMapModel.getLongitude();
        
        // draw at lat,lon
    }
}