It wouldn’t suppress engagement on other posts. Engagement drives reach and visibility. If you post a tweet and it goes viral, it’s not because people are viewing your account feed and viewing what you posted last. People are discovering the tweet via trending lists, people they are connected to engaging with it (i.e when you see “[insert friend’s name] liked this tweet” in your feed.
As a general rule on Twitter, FB, IG – the more a post is engaged with, the more visible and discoverable it becomes, outside people just following your account. Posts that are viral, are usually viral because it’s people who do not even follow you who have seen and engaged with the post. So a new post being published isn’t going to change that or hijack the success of the last. It’s not going to pull eyes away from the viral post.
For content performing slightly higher than average (not viral), i’d still stick with your content timings to maintain the interest your last post has driven. Don’t let people forget you or lose the enthusiasm you drove in your previous post – build on it. I disagree with this “run it’s course” logic.