No, you do not have to wait for the next data refresh of Google to see if a link removal was successful. In most cases, you should see the effects of link building or link removing within a few days or weeks. However, it is possible that some low-quality links may only be re-crawled every few months, which can pose a problem.
To help ensure that your link removal efforts are successful and to avoid having to wait for the next update, you can use the Link Detox Boost feature. This tool allows you to force Google to re-crawl the links that you want, which can help to improve the effectiveness of your link removal efforts and may help to improve the performance of your website.
Overall, it is best to use Link Detox Boost to help ensure that your link removal efforts are successful and to avoid having to wait for the next update from Google. While it is possible that you may have to wait in certain cases, using Link Detox Boost can help to minimize the amount of time that you need to wait and can help to improve the overall performance of your website.