When you use your normal LFS it might be possible (but then you're the host and unless you have a second account you can't join another server (Username in already online or something like that)). With the dedicated server probably not.
And before everyone starts screaming 'ZOMG, a demoër with tweak', I'll tell you why I'm suspecting what I wrote above:
I tried to do the same thing on my testserver (just out of interest/curiosity) when LFS Tweak Z wasn't licence protected. When I started a server from the normal game client and ran tweak on it, players with the exact same car should be able to join (Just like it would be in single player modus, but with more tweaked cars on the track. I didn't really tested the 'letting others join my server' part so I'm not completely sure). When I ran a dedicated server and wanted to connect with the normal (tweaked) LFS it said that the cars weren't the same. And yes, both dedicated and client were on the same computer.