Could invisalign be as effective as traditional braces at treating cross bite?

Ask orthodontist. Simple cross bites involving one or two teeth can be easily treated with invisalign. When you get involved with multiple teeth and huge bony problems, then it's not so clear cut and you may need traditional orthodontics. The diagnostic records done by an orthodontist helps them determine the treatment plan and what they need to do to correct the problem. Ask an orthodontist.
Choices. Both can provide you with a beautiful smile and each have their pros and cons. Invisalign will likely cost you more and take longer, but as an adult you may prefer how it looks while you are in treatment. as far as solving your specific cross bite, you should consult with an orthodontist in person who can assess based on an evaluation.
Depends. crossbites in adults are hard problems to fix. In early teens, it is easily fixed with expander. in adults, to fix it right, normally it is challenging. sometimes we even need surgery. Invisalign can be potentially as effective as regular braces, but that requires %100 patient compliance. If they are not worn all the time, the tx time gets too long or sometimes impossible. Braces don't have that.
No. Braces allow considerably more control than clear aligners. If you have dental crossbite, teeth out of position, your best crossbite correction would be with braces. As an adult, if you have a skeletal crossbite, you will require both orthodontic treatment and jaw surgery. Special skull x-rays required to establish extent of skeletal problem. Make sure you see qualified orthodontic specialist.