Your thinking is correct, and there are a variety of ways to determine the level of interest - or lack thereof.

The first would be the NHC Tropical Weather Outlook - link to the latest discussion is always available at the top of the Main Page.

Another would be the officials, Meteorologists and Weather Analysts on this site - if we haven't commented on a particular feature then I wouldn't get too worried about it. Even when we comment on something, it may only be to note something of casual interest.

Of course if NHC asks NRL to start an Invest on a tropical wave, that usually means that it is a feature that NHC wants to keep an eye on from the standpoint of the potential for future development (and remember, that potential is not always realized).

Finally, we may start a thread in the Storm Forum - often titled as an Area of Interest - when something catches our eye that may or may not develop further. If something develops and threatens, I'll usually post an Area of Concern in the Storm Forum - unless we have it well covered elsewhere on the site - usually the Main Page leadoff article.

Tropical Storm development in the far eastern Atlantic would be a rare event in June - and even if it did form it would still take about 10 days (or longer) to threaten the U.S. mainland, i.e., just something to watch for awhile. A good question, but nothing at all to get excited about out there yet.
Cheers,
ED