I voted no. I didn't find the way the cheats are used here entertaining. I get the impression that this game features plenty of room for interesting techniques and glitches to travel through worlds in interesting ways, but this movie doesn't really show it for me. I'd be interested in seeing a TAS that shows more of the game being played, but that may be just me.
As others have stated already, the rule on cheats isn't strict, but exceptions are rare, and they depend on what the movie aims to achieve with it. Cheats abused to get a faster record than normally possible are generally considered, well, cheating, and henceforth usually aren't accepted here.
A few people have brought up
Biker Mice from Mars, but besides the fact that that movie was judged and published more than ten years ago under a different judging system; it's not a straight up speedrun, but it's more of a demonstration (and is tagged as such). It doesn't aim to get the fastest speedrun time for the game, but it aims to show off ludicrous speed and inhuman course control. Likewise,
Mega Man X's password glitch run, also mentioned, is also tagged as demonstration, and doesn't have the Fastest Completion flag, because it's not considered a speed record.
Now, I fully respect the BfBB RTA community's interest in running this category, and of course they're free to run whatever they like and compete at whatever they like. However, TASVideos has a global set of rules to cover all the games it features, not just this one, and disallowing in-game codes/cheating in most cases is one of those global rules.
Based on the posts I've read so far and based on what I'm reading from the poll, it seems the TASVideos community generally agrees with the TASVideos rule here. It's fine if the BfBB RTA community likes having in-game code categories, but the TASVideos community is a different one, and clearly they largely have a different opinion on what constitutes acceptable cheat usage.