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];
}