local Administrators group is a member of the farm administrators group.
Simple answer is no!
Members of the Administrators group on the local server computer are
automatically added to the Farm Administrators group and can perform
all farm administrator actions
The farm administrator has permissions to and responsibility for all
servers in the server farm. The Farm Administrators SharePoint group
replaces the SharePoint Administrators group that was used in Windows
SharePoint Services version 2.0. Members of the Farm Administrators
group do not need to be added to the Administrators group for each
server. Farm administrators are members of the WSS_WPG and
WSS_RESTRICTED_WPG groups on the computers where Central
Administration is hosted and have the Full Control permission level on
all servers in the environment. By default, members of the
Administrators group are members of the Farm Administrators SharePoint
Members of the Farm Administrators group have no administrative access
to individual sites or their content by default
To add a user or group to the Farm Administrators group and the Site
Collection Administrators group in Windows SharePoint Services 3.0
On the server that hosts Windows SharePoint Services 3.0, click Start, point to Administrative Tools, and then click SharePoint 3.0
In Central Administration, click Operations.
In Operations, under Security Configuration, click Update farm administrator's group.
In People and Groups: Farm Administrators, click New, and then click Add Users.
In Add Users, type the account name for the user or group to whom you want to grant farm administrator permissions. In Give Permission,
make sure that the Farm Administrators check box is selected, and then
In People and Groups: Farm Administrators, in Site Actions, click Site Settings.
In Site Settings, in Users and Permissions, click Site collection administrators.
In Site Collection Administrators, type the account name for the user or group to whom you want to grant administrator permissions for
the site collection, and then click OK.
What i take from that is its the opposite way around :)
Hope it helps :)