If the upper jaw is too narrow then we often place an appliance in the roof of the mouth to expand and then switch to Invisalign. This can take about four months This way you never see braces. On the other hand if the cross-bite is not so severe Invisalign will correct the cross-bites fine.
Lots of things are now possible with invisalign including posterior crossbite correction. Having said that though, there are times when due to severity, number of teeth involved, or arch shape that other techniques are far more effective and sometimes combination therapy needs to be used. Each case is different but having your case submitted to the invisalign computers by your invisalign dentist can get some more definite answers and being open to doing what works best in a particular situation is very important and saves lots of frustration for both patient and doctor.