First of all, welcome to the forum, Fiarrella!
Secondly, yes, it is possible to get children from the Time Machine occasionally. I've never got one, though. But, from people's posts, I figured out that you're usually getting notified by the game if you get a kid. It has nothing to do with traits, it's random. Here's what I've found in the Sims Wiki section for the Time Machine.
It's possible for Sims to meet their previous selves and/or previous companions, and tell them to stop fighting and focus on love and family. If this happens, a Sim may suddenly have a child, but the child will only have one parent.
Occasionally, traveling to the past will result in a message about the Sim using the machine having saved a child in front of his or her past self. This results in a new child being added to the household.
Though, the info on Sims Wiki is not reliable, and can be edited by any simmer, without a reference. You may want to re-check yourself.