This could definitely happen in a catastrophic BCD failure. Being properly weighted would make it easier to recover from such a situation.
It all depends on how one is weighted, from what depth the diver is ascending, and how much positive buoyancy the exposure protection will regain during the ascent.
Every now and then, I see a novice diver (here in SoCal where 7mm wetsuits are commonly worn) do something like what you described. When the diver is ready to ascend, he will exhaust all of the gas inside the BCD, making himself negatively buoyant (sometimes crashing into the sand below), and then swim up from depth against that negatively buoyant force. The thinking here is that the diver will minimize the chance of an uncontrolled ascent, in the event that gas isn't released in a timely manner. Ascending in this way is a lot more work than it needs to be. In fact, it can increase the risk of DCI if the diver inadvertently holds his breath while exerting himself during the ascent. A diver should initiate an ascent while being neutrally buoyant (by inhaling deeply or kicking up a little) and then exhaust gas from the BCD in very small, short bursts as needed. Ascending in this way is nearly effortless and yet maintains proper buoyancy control (being able to arrest the ascent, i.e., get neutral, at any point in the water column).