No, it doesn't. Yes, it does. Hear me out.
Looking at your public profile this is roughly your quality-ban result for Stack Overflow, based on this formula:
(total questions - negative questions - closed - deleted) / total questions >= 0.5:
click image for the actual SEDE query
The deleted posts are the ones that put you in the ban. If you don't have links to them, flag one of your posts and ask a mod for the links.
We are looking for positive contributions to the community. Posting quality content is what we value most. Next to it are edits, voting and flagging. These are all considered positive contributions.
When you are quality banned and are bound to either fixing your old (deleted) posts or relying on the one post each 6 months, you need that time to learn and recognize what quality content looks like and which posts are well received and which ones aren't.
- Suggesting edits: if you improve posts (and keep an eye on the results) you earn a bit of reputation for good edits and you might see posts getting upvotes after you made a clarifying edit. Noticing which posts benefit from your edits and which don't as well as which edits gets approved and which won't will learn you what quality looks like for the Stack Overflow crowd.
- Reviews: By participating in reviewing you get exposed to a variety of posts. You get a feel for your judgement skills and again will be able to distinguish good posts from bad posts. I have a handy user script that shows you your own review result against your peers
- Flagging: Raising flags on posts that don't qualify for being good posts (either for being off-topic / too broad / duplicate or for being non-answers) helps both you and future visitors so only the good content remains. It is highly confusing if the site seem to host both low quality stuff and good content. Again, watching your raised flags page and their resolution tells you if you're on track.
The learning experience from all of the above actions should help you to judge up front if a question you're about to post will be received positively or not. That judgement doesn't come with a low number of reviews in each queue or suggested edits. Think long term, doing your daily allotment for 6 to 8 weeks. If you're planning for the one question per 6 months that isn't much of investment to ask.
tl;dr; Does reviewing posts help? Indirect, yes. But having done 1000 reviews by itself doesn't lift the quality ban.