Can I increase my clock time to affect pregnancy in Fallout Shelter?

Yes. Despite being a key game-play mechanic, Fallout Shelter does not do much to prevent you manually changing the clock to exploit timers.

This should apply to a pregnancy timer; However, this exploit is most popular as a means to rush the production timers, or to farm loot/caps from the wasteland.

Keep in mind that there are reports of this exploit breaking the games sense of time, resulting in some greatly over-exaggerated timers. For example, in one particular case, one of our users experienced a permanent 70+ days added to their wasteland exploring and 1000+ days added to their radio.

This particular exploit is also detailed further on the Fallout Wiki.

Excerpt from the Fallout Wiki page on Fallout Shelter bugs

• Time travel - The core gameplay can be drastically altered by messing with the device's internal clock. Should one set one's clock backwards, all incidents cease unless triggered by the player, and all production rooms gain whatever amount of time that the player went back to added to their next production time. The production rooms can be reset by rushing, allowing a player to collect resources risk-free for as long as the clock has been set behind. This can also be used to manipulate the time Dwellers spend in the Wasteland, but they won't collect anything until the clock has been caught up. The altered time will affect their enemy spawns and loot drops, however, and can also be used to bring them home prematurely by recalling them after setting the clock back and then rolling it forward. Changing the clock or getting to the point in time the clock was changed to originally should fix this highly exploitable bug.[verified]
  • If a room is rushed immediately prior to setting the device's clock backwards in time to exploit the time travel bug, upon having set the clock backwards, the failure rate of a rush for the room in question will have skyrocketed. This is likely because the game gauges rush failure rate based partially on the time since the last rush, and it decreases with time. Since the previous rush is read as having been in the future, the failure chance is elevated accordingly.