No, it would NOT have thousands of names on that list.
I am probably taking the question and the title of this thread too literally, but you have to understand that from the GB's point of view, a partaker is NOT of the 144,000, even if they are baptized JW's.
We all know that there is no way to verify dead "annointed" ones, esp after the 1930's, when JW's started to develop their own laity class.
There is no list of every partaker. There is a list of "annointed" partakers that the GB keeps track of that they consider to be "genuine annointed."
This was not done throughout the history of JW's. I doubt they would claim that the list is all encompasing. (i.e. plausible deniability) But make no mistake that genuine annointed Christians are kept track of. The rest are ignored, other then to count them once a year.
Why else have it as an option to check off if the publisher claims to be annointed or other sheep? It is still on every publishers record card.
Particularly are brothers paid attention to. It isn't a list that they refer to to keep track of all who claim to be part of the 144,000. It is a list to keep track of those who claim to be annointed. Big difference there. It accomplishes two things: 1) Keeps track of potential trouble makers. 2) Keeps track of potential company men as future leaders.