Has anyone let Ross catch them when he escapes at Omicron?  After finishing the game I realized he's actually a non-hostile character.  So why did he chase Simon after escaping the glass chamber and bang on the door of the HPS chamber?

Actually, after you find the items (batteries, cortex chi and structure gel) and is heading back to catherine's room, Ross makes his appearance and say he is coming with you, BUT the Female Omicron Proxy appears and chases you. Just watch the first minute of this gameplay, the youtuber got the items in his previous video and is now heading back to catherine,you will see the female Omicron proxy chasing the player (just ignore the loud effeminate screams)

Roger that,  after saying that I went ahead and played through it again (albeit less hurried this time) and I realized it was the female Omicron Proxy chasing me