The answer depends on where you add column to the Content type - on site or list level. If former, you can update all inherited list content types. Also in this case any customizations you have made to any derived content type will be lost. If latter, you cant.
Take a look at this msdn article. It has great explanation how this mechanism works
The fact that list content types are often derived from site content
types has implications for change management. One consequence is that
customizations to list content types cannot easily be applied to other
lists. For example, a user might edit a list content type by adding a
new column. This change would be limited to the content type on the
list. The new column would not be added to the site content type from
which the list content type derives, nor would any other changes carry
over. Changes to a derived content type are never pushed up to the
parent content type.
However, a list content type can be affected by changes that are made
to its parent. For example, a user could edit a site content type,
perhaps by adding a column, and then choose to update all content
types that inherit from it. The result could overwrite customizations
that users have made to derived site and list content types. It is
possible to protect a content type from receiving changes that are
made to its parent, but this step has implications for content type
management. For more information, see Content Type Change Control.