1) Depending on the location of the cavities, the fillings could impact your Invisalign treatment, especially if you have many Invisalign molds that have already been pre-fabricated. This is due to the fact that Invisalign wraps itself tightly around the surface of individual teeth to cause their displacement. Any change of tooth morphology ("Shape") could have an impact on how well the Invisalign sits on the teeth and compromise its efficiency.
2) Depending on the depth of the cavity, the dentist could decide to monitor the cavity instead of immediately filling it. If dental hygiene is improved, the cavity could stop growing or in some cases the cavity can remineralize. On the other hand, if it is too deep, it is more urgent to fix the cavity than doing the Invisalign treatment. Keep in mind that if a tooth is damaged, there is no sense in moving it around in the first place.
To conclude: Dental Hygene is crucial during ortho treatment, since the ortho appliances, including Invisalign can Harbor food debris and bacteria, as well as hamper the cleaning action of saliva, causing an increase in the likelihood of getting cavities. Communication between the orthodontist, the dentist and the patient (you!) is very important. Everyone has to be aware of each other's wants, needs and actions. If you don't let your dentist know you are getting an orthodontic treatment or you don't tell your orthodontist that you had fillings done, there is a possibility that they won't become aware of a problem which could result in additional fees, and delays in the treatment plans.