Actually yes if you stuck to it then it would but the chances of sticking to that plan are virtually zero and I will tell you why:
Firstly 600 is a terribly restrictive amount, within weeks you will feel extremely unwell and have extreme hunger, you are likely to end up binging at this point so that's the plan gone already.
Secondly even if you did stick to it, having lost the weight you will now have a slowed metabolism and a body that is depleted and suffering from extreme starvation and malnutrition, at this point I promise you will binge if you've made it that far, also your slowed metabolism will mean that in the early weeks even a gradual increase can cause quite a bit of gain, most will be water and yes it does settle then you lose again but you have to keep repeating that cycle until it evens out.
I have restrictive type anorexia and relapsed badly a few months ago, I got through 3 months of painful hunger because anorexia doesn't lay off easily so you can't just choose to stop, anyway I was on 500 calories a day at most, I was told to increase by 100 a day at first because if you restrict that low then eat too much you can get refeeding syndrome which is rare but potentially fatal.
I started increasing last Monday, last night after 3 months of crying with hunger because it gets that painful I binged, now this is coming from someone with anorexia, someone who has a powerful disorder that is hard to fight and binging does not come easily, it is a reactive action actually and very common after restriction, it's not a lack of willpower or anything, it's just because if you starve your body it's going to kick your backside with werewolf type hunger when it can no longer take anymore of it.
I am underweight so gaining weight wont hurt me anyway, in fact I had this during my last recovery and never went over a BMI of 20.5 but only because my BMI was dangerously low when it started, if I had had a BMI of 20 and starved myself to get there then I would have ended up overweight because I was eating 10-15k calories some days and you might think you'd never let that happen to you, I thought that too, I would chew gum, go for a walk, do anything to try to stop it but your body is a smart machine and it will override you, I fought with all I could not to binge but couldn't help it, I would throw out food then go buy it again.
You honestly have no idea of the absolute hell you are thinking about letting yourself in for, the correct way to lose weight is never to starve and restrict, you should actually aim to lose it on the highest amount of calories possible, it is healthy, you wont damage your metabolism and treated as a lifestyle change and not a diet it is also sustainable and has a very high success rate at keeping the weight off, that is the right way to do it.