You can safely place the implant right away before or while you are in Invisalign/orthodontic treatment.
The premise of Invisalign therapy is that one can use a computer model to predict the position of the teeth prior to movement. This is how the aligners are manufactured. It is possible to predict the final position of the tooth and place the implant accordingly.
We use implants in conventional orthodontics (regular braces) all the time. If the implants are placed in the predicted, desired position, after proper, careful planning, the orthodontist can actually rely on them for the movement and the process happens much faster. I do recommend fabricating the final restoration after the Invisalign treatment is finalized, yet prior to delivery of the retainers.
Consider contacting a surgically trained Prosthodontist (the specialist in restorative/cosmetic/implant dentistry) for this work, since it is the most qualified person in this field. Since the Prosthodontist is the restorative expert, he/she will be able to place the implant in the most optimal position, so that the final crown is properly fabricated. You can easily locate a Prosthodontist near you on the internet.
Best of luck with your treatment,