Invisalign is a great tool to straighten teeth and correct certain bite problems. It is an excellent appliance to manage open bites and can successfully correct some open bites. The key to good success is to use an orthodontist who is well versed in using the appliance. Ask him or her to show you similar cases such as yours. Like a paintbrush, a tool is used with varying success in different people's hands.
Here are some Q&A's that talks about that:
Invisalign for Open Bite Correction?
Will Invisalign Fix a Misaligned Open-bite?
Posterior Open Bite- Already Began Invisalign Treatment, Should I Be Concerned?
Here are some Invisalign reviews of people who mention having an open bite:
“Invisalign Fixed Upper Teeth but It's Not Good if You Have an Open Bite”
“Hoping for a Straight Smile and Fixed Open Bite"
Invisalign Process for 40+ Year Old Professional