Effective question @diwz
If you requested to Google to take an action on it, if that is your own web page so you can submit this request directly to your webmaster account. Google will review the entire strategy and will proceed this request as soon as possible, there is no particular time so estimated time that we experienced is within 72 hours.
That will not impact on your search engine rank, instead if your 404 page exist for long time so that can put down your web rank in search engine. So don't be panic, but try to resolve crawling errors quickly with in 24 hours duration. Hope that will help you!