I have traveled and gone to work while the machine was running, and didn't have any problem. Several times I loaded my home machine, went to the community maker's space, fizzed up batches in both machines there, and came home. When I got home, the machine wasn't done, so I guess it does pause while you're gone, but it finished up without a problem. I haven't done a GTW career with it running, but rabbithole jobs haven't been a problem.
BTW, thanks for the Growfruit info. I aged up the baby to toddler immediately, because I'm not a fan of crying furniture. I aged her up again as soon as she maxed all skills, because toddlers are a real PITA. But now it's winter, and a winter vacation to Granite Falls is pointless. The river is frozen and all the plants are dormant.