Yes, producers do time their productions but for a variety of reasons.
First of all, anime are released quarterly. This means you have a seasonal release beginning with winter in January, spring in April, and fall in October.
To resume it, I would say that usually the biggest blockbusters are released either in summer or fall, since after a big investment, producers would need to sell a lot or get big audiences, which is accomplished by releasing the material during vacations when there would be more people available to consume the product, as it's usually everywhere. However, this rule is not set in stone and there are many other factors that influence when exactly producers decide to broadcast an anime or to release a light novel or a manga.
Right off the bat, if a certain anime season takes place within a specific season, then the producers will time the release of the production to the season in question. For example, the second season of Suzumiya Haruhi begins with a summer festival episode about Tanabata. The next 8 episodes called Endless Eight are all about the main character being trapped in an endless summer. The first episode of Endless Eight was broadcasted on June 19 all the way through August. Since the plot of the episodes revolves around the protagonist being caught in a time loop because he hasn't done his summer vacation homework, the 8 endless summer episodes were broadcasted during the 8 weeks of summer vacation.
On the other hand, an anime like Yuri on Ice began broadcasting in the fall so that the climax of the season would be around Christmas which seems like something logical for an ice skating show.
Many anime about high school will begin with the school term, that is in April with spring since this is also the beginning of the Japanese school term. Almost all high school animes are about club activities (like Suzumiya Haruhi). In this way, the first episode of spring coincides with the beginning of school terms for kids in Japan when they will also, most probably, join a sport or cultural club. Examples of this are Hyoka (Classics Club) or Euphonium (Band). Spring anime is thus slanted toward SOL anime or school anime. This gives it in my opinion a more comfy vibe since you get more comedies.
Likewise, sports anime will be broadcasted in the season when they are played. Baseball shows will tend to begin in spring or summer. But if you have a very long story arc like in Major, the show might begin in the fall, so the last episodes are broadcasted around April when you will have the big tournament. It makes sense to want to match your "Koshien" episode with the real Koshien.
Since an anime, like a school anime, can span more than one year, the producers will usually use either the first or last episode to time the release. Also, it depends on the motives. Beginning a show in spring is usually adequate to introduce new stories and new characters. Whereas beginning broadcast in the fall means that the last episode will be broadcasted during the end of the year, which is a good time to wrap up or finish a story.
So if an anime covers a long time span but the last episode is set in Christmas or new year, it's very likely that for this reason alone it will be broadcasted in fall, rather than spring or summer when you would expect bigger audiences, since you can still make use of the end of the year holiday.
So in conclusion, there are an infinite number of reasons why producers decide to release their content in any given season. This doesn't mean that there are fixed rules as to when an anime of a certain genre has to be released. In reality, it depends mostly on the story. However, you can see that animators are really careful to try to time their releases at the best possible time, so as to cause the best possible impression with the audience and thus drive higher sales.
