Based on the wording of your question, I can't see a way today to prove it never could, therefore the answer currently must be "Yes, it may someday be possible."
Note: This assumes that "conscious" as defined in this context is specific enough for the question to ever be meaningfully answered "Yes." This is a non-trivial assumption because there are criteria by which some would judge AIs as already conscious. Alternatively, some philosophers of mind have criteria by which they assert humans aren't conscious.
The differences between ChatGPT and a conscious human brain are not unsurmountable.
Let's consider a potential future conscious AGI created by advancing from something like ChatGPT.
The human brain is "always on". It's possible to have a digital system be always on, i.e. not just train once and then just respond, but constantly take new input.
The human brain has way more connections/layers than ChatGPT. It's possible to imagine the digital system getting the same number of connections.
The human brain gets real time sensory input. It's possible to add cameras, microphones, etc to that digital system so it gets a constant feed. Maybe even let it process what it saw during the day in a batch training/GC run (we could call that "sleep").
The human brain has a different topology. It's possible to alter the topology of a digital system neural network to mimick that, instead of using the ChatGPT topology. It's not like we're forever doomed to its simpler statistical model. But it's interesting that it already gets very significant emergent intelligence-like properties.
The human brain is self-conscious. This can very well be an emergent property of the above. I think all that's needed is the ability to have some form feedback mechanism.
Is there a consensus? I haven't been able to find much else via Google search. At that level of theorizing I wouldn't expect any consensus, only original ideas from a few elite researchers.
I have a feeling it's like the saying "Any sufficiently advanced technology is indistinguishable from magic". At a certain point they could become practically identical things.
Note: This assumes that "conscious" as defined in this context is specific enough for the question to ever be meaningfully answered "Yes." This is a non-trivial assumption because there are criteria by which some would judge AIs as already conscious. Alternatively, some philosophers of mind have criteria by which they assert humans aren't conscious.