In my opinion it is possible, but the only way is to force proxy browsing by setting rules on the firewall, as explained here:
This (related to IPFire), I believe applies to any operation that requires blocking Web sites or services.
With the same system, I think you could block Reddit as well. 
If you want to block only Reddit, once everything works, you can act on the url filter by creating custom rules. You can also enable browsing to all sites and block only those sites that are “hostile” to you. Remember, however, that the “impractical” thing is to set a proxy in all clients. And it cannot be done otherwise. This can often be annoying, but it is essential for everything to work.
Alternatively, if the site to be blocked is only Reddit, you can track the IP address and block only outgoing traffic from RED to that IP. Many times I have solved this way, but keep in mind that the IPs of sites can change or be in a high range. This is impossible to control with firewall rules alone.