Ed,
Automated Tropical Cyclone Forecasting system. This system coordinates all tropical cyclone products, databases, and help initiate forecast model runs (say the GFDL). To track and start looking at hurricane models the specialists at NHC, CPHC and JTWC will start these invest systems. Still a weak disturbance can be "tracked" w/o being started in the ATCF. JTWC has a history file back through disturbance IF the cyclone becomes warned upon ie given an alphanumeric (01W or 01L) on their web page. I don't believe finding NHC's ATCF information is very easy, even after the season. Still I can give you some of the information you seek.
In 2005, 30 systems had bulletins issued on them in real-time indicating TD strength or higher. 1 system was "upgraded" into the historical database (HURDAT) as a Sub-tropical Storm ("31"L)...you can find a write up on NHC 2005 historical archive page.
I cannot be 100% sure, because I only keep track of Dvorak classification statistics for SAB... but I believe we went through the list 90L-99L Four times, and I have a 96L just before 28L, 29L, and 30L... so assume we got to 99L (as Zeta would have formed from 99L). So that would be 50 total invests. 30 were warned upon, and I have 14 invest areas that were classified by SAB and/or TAFB. This would logically lead to 6 systems that were invests that never were Dvorak classified (or Sub-tropically classified). Yet, 27L (Gamma) was actually an invest area twice... so after all this I have a grand total of
19 Invest areas that did not reach bulletin strength.
Additional to that, there were 3 other systems (that were not designated as invests) but were classified by SAB/TAFB. This included the STS 31L that was later added to the official 2005 storm list.
So were there 22? How about other storm clusters that were not tracked, classified or invested but may have been worth noting? The options are endless and to the point of getting into back ground noise. So it may be a point of note or interest, but I hope you don't try to make some scientific theory or hypothesis based on these stats
Not trying to be a spoil-sport, but don't want you to go to too much effort over something that is arbitrarily determined.