Can invisalign work in my case in order to fix the black triangle? Is IPR necessary in my case? (Photo)

IPR is sometimes necessary to achieve optimal results and give your teeth room to move into place. IPR only reduces the enamel by millimeters...very small amount of enamel is removed, not enough to be concerned about. There is no stripping of teeth done when it comes to this. 
The black triangle can be reduced or minimized with invisalign. Each invisalign case has steps to reach optimal results and IPR might be indicated. You could also try bonding with resin composite (tooth colored filling material) and enamelplasty (re-contouring) on the teeth. The dentist can re-contour the teeth and add filling material to close the dark triangle spot. Another option is cosmetic veneers or crowns to change the entire look of the teeth and remove the black triangle. That option is more invasive and costly.

Treating the "black triangle" is easy with Invisalign. but more importantly treat the cause. A close look at your photo as well as the black triangle indicate  you are having gum recession.  This is caused by Periodontal pathogens and your immune system.  A good dentist should be identifying and be helping you eliminate these causative "bad" bacteria.  If your current dentist is not using a Phase microscope or any other identifying technology nor using antibacterial therapy to eliminate these pathogens, I would predict you will be getting bigger and more "black triangles".  For some more information on this see the video on Vimeo by typing in Oral Pathogens - The Silent KIller,  or on YouTube by typing in Periodontal Disease - The Silent Killer.   You can also see the video aimed at public education on the Periodontal Pathogen Public Education Foundation website. 

invisalign will not correct the black triangle and I would not do IPR on your front teeth.  This would destroy the natural emergence of the tooth.  All is not lost though.  There are 2 ways with possibly dealing with this.  The least intrusive is using fillers to fill the papilla.  If done correctly, it can result in a nice result.  May need to be done a few times, but if there is no underlying bone problems, it will gradually rebuild the papilla. 
The other way is to have a specialist (periodontist) evaluate the area for possible esthetic periodontal surgery.
Good luck