If posts are spam, let's report them and the spammer will come to a ban soon.
A little bit beyond this case, you can see a user makes a series of post but if these posts are good in quality, it's not a spammer and no issue at all. Assume he composes these posts and when are ready, he releases it in a series. This style is not common but I would like to give the example to show that quality is key of deciding a post is spam or not spam, should be deleted or kept and a poster should be banned or not.
I understand what you meant but there's actually more to it;
This forum doesn't actually accept schedule posting, if it does, we can say that a user at his leisure could make like 20 posts and schedule them to be published later. In the scenario you painted that someone could make posts and later begin to post them one after the other, to me I may consider this as a type of spam.
Spam could also be doing things in a sequence that negates the natural way of doing things in a particular environment. In the issue in question, the time between posts is 2 to 3 mins, this could also suggest that this is a bot operation.
But in all, I don't want to belong to a forum where people are interested in quantity discussion and not the quality of the discussion.