Do you mean on your computer ?
Yes, another user could install a firewall on your computer and set it to block access to the internet or e-mail from your computer.
Having said that, as a user of that computer you should be able to change any setting on that firewall so you should be able to allow access to the internet.
Also, if your computer gets access to the internet VIA another computer (as it may in a network) then they could set a firewall up on THAT computer which would also block your access to the internet and e-mail.