yes...you can type 'demorec' in the console and it will record.
It will save them to - C:\Program Files (x86)\Steam\steamapps\common\TOXIKK\UDKGame\Demos
Then you can type 'demoplay' filename in the console to play it. You can use 'behindview' to view from behind (a bit jerky though)...'behindview 0' to toggle it off and 'demostop' to stop it.
Use fraps or similar to capture it to video. I rather like the third person view because you can do multiple captures of the same battle from different POVs so you can edit in some really cool cuts between multiple perspectives.