There are periods where contact is prohibited and periods where contact is limited. You may want to visit the NCAA's site to download their whole brochure on this subject, because it's too complex to digest here.
What I can tell you is, the rules apply to THEM, and not to your son. So your son has nothing to lose by contacting people, and if he is genuinely interested, periodic contacts are a good practice to let them know he remains interested. Of course, anything can be overdone, and it seems you are already aware of the risk of becoming a pest, so follow your instincts there.
Just understand that if you don't hear back immediately, they could conceivably be in a quiet period, unable to respond. Or they might just be on vacation, or otherwise slammed with pressing work. But eventually if they don't respond, you either need to follow up or perhaps read between the lines.
AL MA 08, if the schools your son contacted have replied expressing interest, and if you are indeed interested enough to be willing to make time to visit (and to shoulder the expense), a good way to open the lines of communication is to ask if the coaches are planning a "junior day". If they are, you might find your son invited; don't be shy about asking. If they aren't planning a junior day, they might still suggest an individual "unofficial visit", i.e., a visit you pay the expenses for. These can be even better than junior days, because you get one-on-one time, as opposed to coming in a group.
While there is lots of time, you should also know that many schools are already extending offers and not all of these offers are going to headline players. Some are for guys that fit a particular need at a school, guys the coaches feel good about, and guys the coaches know can cut the mustard academically. Sometimes coaches feel like they have a "find", someone who's been overlooked on the ranking lists, etc., maybe a local kid who hasn't done a lot of travel ball, and they may want to lock him up before others lure him away.
If your son needs time to figure out what he wants to do, fine. But if he's ready to talk to his favorite schools, there's no time like the present to get started.
One thing we've seen is, everybody always needs pitchers, but sometimes teams need a 2B and sometimes they don't. If your son is a pitcher, then he may have more options. If he's a position player, then getting a jump on others is a good idea because your favorite school might otherwise fill their need before you get there.