/nerd hat on
Technically, its not really a virus, but a worm that appears to have the intended purpose of creating a botnet by the hacker.
/nerd hat off

If true, they are less likely to try damaging your machine at all beyond trying to prevent you from finding or removing it. Botnets are increasingly used to make money for the hacker, and they don't make money if your machine doesn't work. They are typically (not always) used for spamming, brute-force attacking other systems (dictionary attacks, for example), or other purposes that benefit from having multiple machines under their control.

When they say that all these copies become "active" on April 1, all that means is they are all now trying to phone home (the hacker) to request instructions on what to do next. They basically sit there doing nothing but saying "awaiting instructions...". The hacker can now send out whatever commands he wants to these machines when they like.

EDIT: You can read up some more at http://en.wikipedia.org/wiki/Botnet, where they even have a chart that shows Conficker's stats compared to other known botnets. Keep in mind that all versions of Conficker (a, b, and c) are all considered part of the same structure.