Do I have to wait for the next data refresh of Google to see if a link removal was successful?
No. Usually you should see effects in link building or link removing after a couple days or weeks. Of course very low quality links are only re-crawled every couple months, which could pose a problem.
Use the new Link Detox Boost to be better safe than sorry and waiting.
It can happen in certain cases that you will have to wait for the next update.