Not necessarily. I went into my AOW wearing 24 lbs of lead in cold fresh water with a full 7 mm farmer jane wetsuit, hood, gloves, and boots, a petite female, weighing a little over 100 lbs. I did my first weighting check ever during the AOW, and sank 10 feet with an empty bc and holding a normal breath. I went to remove weight at the shore beside us and the DMC said, "It's ok, it'll even out by the end". My buddy and I did the navigation with the DMC, and she didn't like my trim, so she kept asking her husband, a DM, for more weight to hang on me in various places - totalling 33 lbs, which felt awful. My ladies BC had a lift of 25 lbs. The instructor was in the general area, within 50 feet away, with other students.
I then went to do the peak performance buoyancy with the instructor through hula hoops, and it was a nearly impossible constant extreme challenge managing the air in the bc. I finally signalled to the instructor to watch me and I laid on the bottom and fully inflated my bc, obviously burping it many times, and still flat on the bottom. He just looked at me and shrugged his shoulders, apparently not understanding that I looked like a christmas tree with all the hanging weights. I had to kick to initiate an ascent. Afterwards I told him that I am extremely overweighted, and wanted to take all the extra weights off and he said "No, keep them on".
During the night dive, where we were supposed to stop and hover at 30 feet, I could not stop my descent with a fully inflated bc and the 33 lbs of lead and went freefalling to the bottom at nearly 60 feet, with the whole group coming with me. Nobody stopped before the bottom and everyone failed the night dive.
The second day the co-owner was there and saw me about to get into the water and couldn't believe her eyes. She asked me how much weight I was wearing. I told her 33 lbs and told her I sank 10 feet during the weighting check with 24 lbs. She told me to take all those weights off and go down to 20 lbs. I was so relieved. I asked if I could try 22 lbs since I had a hard time descending. She said ok, and took me for my multi-level dive. She said we would not go past 70 feet on the first dive and see where I'm at, although she knew that I was OK before the AOW. She taught me tricks to descend efficiently, hover motionless, use my lungs proactively, and kick efficiently - all in one dive. With the descent techniques she taught me, she asked me to try 20 lbs on the next dive, the deep dive, and I did, and for the first time, I knew what it felt like to be perfectly neutral. She had me hold various stops without a line horizontally and motionless, and I was amazed at how neutral I was.
That evening we all repeated the night dive with some actual instruction and all went well. The third day, I did my 2nd and 3rd deep dives for the deep specialty, all went well, and I passed the AOW and Deep specialty. Thanks to one dedicated and fabulous instructor. Yes, I told her that most of my skills were done with the DMC, not the instructor, and she was appalled.
So, the point of my long story is that some students may be so grossly overweighted that a fully inflated bc cannot lift them off the bottom. And some instructors don't recognize this or don't correct it.