It is possible and has been demonstrated. However, a virus on Linux could
only do what a the user executing it can do. Usually, that puts a limit
on spreading the virus. For example, it can't infect /usr/bin, as the
user can't write the files over there.
If a virus is executed by root, much more is lost. For example, if the
virus sets itself into /lib/libc.so, every dynamically linked program
is instantly infected.
Regards,
Martin