A lot of different products can be used for scar management, this is one of them. I believe they are now recommending keeping them on for longer timeframes to minimise scarring. I'm not convinced that any product would stay on for a month af a time. We used to use similar products on burns and grazes, and they didn't stay on much longer than a week or 10 days at best. Mind you, these were often on knees and hands, and other very exposed parts of the body.
As far as having it on during radiotherapy??? Not sure, but suspect not. Do you have a breast care nurse you could speak to?