Yes, it is safe to go through the aligner process during pregnancy. However, pregnancy is a time of many physical and hormonal changes. As a result, some women experience tenderness of the gums, gingivitis, morning sickness, and other issues. This may mean that aligners may sometimes feel more uncomfortable or tighter than they would otherwise, and you need to take extra good care of your dental hygiene.
On a positive note: Your aligners can protect your enamel from those strong stomach acids! Just remember to remove the aligners after you've been sick and to rinse both your mouth and aligners thoroughly.
And since you're probably already feeling a bit uncomfortable - why not end up with a new new baby and a new smile at the same time!