If you are doing your drawing in drawRect: then the answer is NO. You will need to rebuild and reposition your path each time. What you can do is something along the following lines:
- (void) drawRect:(NSRect)dirtyRect
{
    // Assuming that _relPos with x and y having values bewteen 0 and 1.
    // To keep the square in the middle of the view you would set _relPos to
    // CGPointMake(0.5, 0.5).
    CGRect bounds = self.bounds;
    CGRect rect;
    rect.size.width  = 100;
    rect.size.height = 100;
    rect.origin.x = bounds.origin.x + bounds.size.width  * _relPos.x - rect.size.width /2;
    rect.origin.y = bounds.origin.y + bounds.size.height * _relPos.y - rect.size.height/2;
    NSBezierPath *path = [NSBezierPath bezierPathWithRect:rect];
    [[NSColor redColor] set];
    path.lineWidth = 2; 
    [path stroke];
}