Yep! Sharing Tweet IDs (and or user IDs) is the preferred way to share twitter datasets: Twitter and Open Data in academia
I’m not aware of any restrictions on how many tweet IDs you can share - but the ratelimits for downloading tweets in bulk may put a practical limit on that. As an example: with https://dev.twitter.com/rest/reference/get/statuses/lookup you can download 1,728,000 tweets in 24 hours - if you also use application authentication, you can get up to 2,304,000 in 24 hours.
How many days someone is willing to wait for a dataset to download depends on how interesting the data is…
Not sure if anything’s changed recently, but it should be fine to share derivative data - A database of status an example might be hashtag counts over time, or this giant language model, because that doesn’t have the original tweet text. But even then, it’s nice to have tweet ids to go along with the derived data.