For a spa, it is important to turn it off as you suggest. Otherwise, the circulation pump alone is enough to heat the spa perhaps to 80ºF or so which will be warm enough to deplete the chlorine too quickly. If you let the water cool off to a lower temperature, the chlorine should last longer and you may get it to last the month.
You can do a simple test before you leave where you check the 24-hour chlorine loss in the spa. Let's say that was a 5% loss of FC. Then 30 days would be 0.9530 = 0.21 or 21% so if you started with 10 ppm FC you should have around 2 ppm FC after 30 days. However, if you have a 10% loss of FC per day, then you would have 0.9030 = 4.2% so 10 ppm FC would end up with 0.4 ppm FC so not enough. So you can see how sensitive the situation is to the daily chlorine loss rate.