Is it possible to prevent the game from pausing when window loses focus?
Yes, it is possible to prevent Skyrim from pausing when its window loses focus.
Open Skyrim.ini (in Documents\My Games\Skyrim) and add bAlwaysActive=1 under the [General] section.
Source: https://www.reddit.com/r/skyrim/comments/1tqcbo/howto_alt_tab_without_pausing_the_game/
Now, you can alt-tab and the game will continue to render in the background. I recomend running in (borderless) windowed mode so you can see what is happening. I find this very useful for letting my housemates play on the TV while I do work on my other two monitors.