Teeth shift all the time, they can shift in weeks. Most likely the shifting would be minor, but you risk the aligners not intimately fitting. In order for Invisalign to fit well, you want your scan as current and accurate as possible.
Can you upload a picture? Depending on the situation, matching the teeth can be extremely difficult. The dental technicians that make the crowns vary in their skills. In order to get a perfect shade match, your dentist may need to use a different technician or lab to get the results that you desire. Also, to get the best match, the highly skilled dental technicians charge a premium. Often, the patient will pay additional lab fees for a perfect match. Enamel is translucent and reflects and refracts the light. Dental porcelain is not translucent. To answer your question, doing 4 or 6 teeth will be easier for the less skilled technicians to match. If I were you, instead of doing more crowns or veneers, pay more for a better lab technician.
Invisalign is a viable option if you have bridges in the front or the back. The problem that you and your dentist will face is moving the bridged teeth. You can't move teeth that are part of a bridge. Sometimes the case can be completed without moving the bridged teeth, but it can limit your options. The same goes with traditional brackets and wires, you cannot move bridges or implants for that matter. Given that you have headaches, it is possible that your bite is contributing to the headaches. With that being said, ideally you would have your dentist cut the pontics off the bridges, complete Invisalign and replace the bridges with new bridges or with dental implants. The pontics are the portion of the bridges replacing missing teeth. To answer your question, yes you can do Invisalign with bridges, but it may limit your results.