Speedrun.com doesn't support speedruns of several games in succession and Don't Escape Trilogy page if ever made will create too many complications you might be unaware of so I highly doubt that it can be a thing.

Although, nothing stops you from making this type of run for a stream/video. Trilogy/Anthology Run will have a great entertaining value and if you will manage to get a WR on any individual game it would be even better.

Why there is no category for classic Blizzard maps like StarCraft Master or for Left 2 Die? There are more actual speedruns done for them than for some of the individual levels of campaign here. Even Lost Viking is partially speedrunnable. Why not just to have categories for that? They would make more sence than coop category in LotV in current state.