Tente isto:
vzctl enter $VM --exec "apt-get update && apt-get upgrade"
O & & significa "Se o comando anterior for concluído com sucesso, continue para o próximo."
De link :
exec CTID command
Executes command in a container. Environment variables are not set inside the container. Signal handlers may differ from default settings. If command is -, commands are read from stdin.
exec2 CTID command
The same as exec, but return code is that of command.
Por outro lado
enter CTID [--exec command [arg ...]]
Enters into a container (giving a container’s root shell).
Option --exec is used to run command with arguments after entering into container. This is useful if command to be run requires a terminal