A committed individual or organization could easily aquire network storage in the Petabytes. I think that would be more than enough to get a sizable operation started.
1 petabyte is 10
15 bytes.
There are 2
160 possible BTC addresses, each of which is 160 bits == 20 bytes long.
So to store all of them you need 2
160x20 bytes, which is 29,230,032,746,618,058,364,073,696,654,325,660 petabytes.