I think this is a great idea. It won't kill your approach anxiety all together but it will definitely help. No one thing will ever kill your approach anxiety, it's a combination of so many other things.
I didn't do the 30 day challenge, instead I challenged myself to talk with everyone when I went out. It was kinda rough at first but I eventually got it down.
The biggest challenge for me was approaching women that I didn't have the ability to walk away from. For example, talking to a girl in a long line that is next to you. On a street approach you can walk away but in a line you are forced to be around that girl for 5-10 minutes if it goes badly.
I disagree with Lord on it needing to be a positive experience. It could make you feel worse or better if you get rejected depending on how you frame it. You could take it personally and think your 'game' is horrible. Or you could be use the situation to getting over your attachment to the outcome.
This might help you to get over your attachment to women:
Going down in flames