Did the Dr. mention why the bone has receded in that area?? Bad tissue loss is caused by bone loss in the area. Most often due to infection in the area. Crown lengthening is going the wrong way, you want to go coronal, not apical.
You might want to talk bone grafting with a gingival graft in the area to try and bring the bone level back up. Theoretically, the titanium of the crown wouldn't be a hinderance, but I don't think I have ever read of a study that would point to it helping. Additionally, if it did adhere to the crown, when you lost the tooth, you would be ripping all that bone growth out, as it will be attached to the titanium, negating all your hard work. But aside from that...
There isn't a good chance of the bone growing up to the height you are hoping for without doing some grafting. Vertical bone growth, even with grafting, is one of OS's most challenging areas. Remember, osteoblasts work best to form new bone when they have a matrix in which to operate. Think of rose bushes on a trellis. Without that matrix, the osteoblasts can't deliver blood and nutrients as readily, and the growth is stifled.
If it was me, I would weigh the effort and cost of trying to save that tooth vs. extraction, proper grafting, and implant placement. Long term, the implant will probably last longer.