Can breast implants be added at the same time they remove a chronic abscess with granulation tissue?

It would be much safer to wait to do the implants. You should wait 3-6 months at least to let the inflammation recede and scar tissue soften up. This will give you a safer path to a better result. Best of luck on your journey. 

In general, it would not be wise to place breast implants at the same time as dealing with an infection of the breast as it would have a high risk of getting an infection around the implant and require removal of the infected implant.It is best to have any infection issues resolved totally and let the breasts be infection free for a period of at least 3 months (many surgeons require at least 6 months) before doing an augmentation with implants.Please consult with an experienced board certified/eligible plastic surgeon who can give you advice in person, tailored to your particular situation.  Than you.

I would not recommend placing implants when there is active infection in the breast.  It would be much safer to wait for at least 3 months after the infection before placing implants.  It will be much better for you in the long run to be patient so that you can have a great result without a high risk of complications.