Yes, all the pending runs per game are visible with the API. And for per user: this can be seen on their profiles.

Speedrun has an API? Where can I find it?

API v1's docs can be found here: https://github.com/speedruncomorg/api

But this API is old and isn't maintained. So I'd recommend to use SRC's API v2. Which is what the site uses internally. This can be found by using the network tab in a browser's dev tools.

There's also a community-made documentation for API v2 here: https://github.com/ManicJamie/speedruncom-apiv2-docs

And there's also a Python wrapper, which I find useful: https://github.com/ManicJamie/speedruncompy

The developers have also said they want to make this public in the future. However, I'd imagine this wouldn't be for a long time. Also, you woundn't get banned from the site for using this.