No for Adobe software
I have seen mention of specialized computers & software, I think starting at $50k per seat, but did not make note since I am not a Hollywood studio
Adobe Media Encoder (AME) does not support automated distributed rendering, so neither does Premiere Pro. However, After Effects uses its own encoding engine and will happily do network rendering to still image sequences - see the AE help file for more info.
If you're working in Premiere with silent footage that has very complex effects, because AME can export to still images it is possible to manually set up a farmed render on a PP sequence; by copying the entire project to each workstation and setting different frame ranges for each one to export. You'd then bring all the image files back to a single workstation for encoding to video, but you're only saving time on the effects so the sequence has to be monumental for it to be worth the time and effort to set up each job.
In contrast, After Effects' effects can take a very long time to render and are always applied frame-by-frame, which is why it can support distribution. A single seat of AME with access to decent hardware (including CUDA GPUs) can convert those stills to a video file extremely quickly.
Distributed rendering of video isn't a widely-used concept, as the compression processes don't like frames arriving out of sync. There are a few solutions which can farm the video encoding step, such as Promedia Carbon, but they're strictly the domain of studios (you're looking at tens of thousands of dollars in licenses, even for a small network). They're used for transcoding rather than rendering (e.g. converting tape library footage for the Web, telecine and pulldown).
When performing distributed processing of video (Apple Compressor does this btw), there is an extra step where it has to piece back the separate parts into a single movie. This can sometimes take longer than the encoding process. But there can be an appreciable time saving for longer movies (30 mins+) so it's a feature I'd very much like to see in AME.