Short Answer
This question reduces to:
"Could a language-proficient algorithm ever be conscious"?
Answering this question requires answering the question "what is consciousness, and what causes it to manifest". There is no consensus among philosophers, or scientists on this question, so the answer today has to be "we do not know".
Longer Answer
Philosophy of Mind has been the dominant area of activity among philosophers for the last 3/4 of a century, and this has been because the difficulty of understanding and predicting consciousness has been the most notable challenge to the dominant ontology of physicalism. This is called the Hard Problem of Consciousness. Philosophers have pursued multiple approaches to try to resolve this challenge. Currently, there is no consensus that any of these avenues will close, and each of them have different answers to your question.
For reductive physicalism the proposed answer is that the processor hosting the AI chatbot could become conscious.
For emergent physicalism, some aspect of the structure of the processor hosting the AI chatbot could allow the processor to become conscious.
For algorithmic identity theory, the algorithm of the chatbot could be conscious.
For algorithmic emergence theory, some modes, functions, or structures of the algorithm could allow consciousness to emerge for the chatbot.
For fusion theories (Integrated Information Theory is a fusion of algorithmic and physicalist thinking), a chatbot with specific structure, AND specific algorithms, could be consious.
For delusionist physicalism, humans are not conscious, and while it might be logically possible for an AI to became conscious, there is no reason to expect this to happen.
For neutral monism, there is an automatic coupling of consciousness with all physical objects, and the processor hosting the chatbot is already conscious today.
For consciousness-based idealism, it is an open question what the relation between the chatbot algorithm, or its processor, is with consciousness. Some idealist speculations limit consciousness to pre-existing agents, in which case the chatbot would never be conscious, and others are universally pan-psychist, in which the current chatbots (either through their processor, or thru their algorithms) already are conscious.
For interactive spiritual dualism, the physics of what could become ensouled and therefore become conscious is an open question, and either an algorithm, or a processor, could possibly be structured such that they could become ensouled. In general, our processors and algorithms of today are assumed to not currently host ensoulment very well, or at all.
For interactive emergent dualism, the physical (or algorithmic) structure needed for consciousness to emerge and become interactive is still TBD, but once we discover what it is, then either the algorithm or the processor for the chatbot could become conscious if we implement that structure.
These answers are all over the place, ranging between chat bots already being conscious, thru there being no consciousness even in humans. However, most of these Research Progrmmes postulate that the answer will at some point be "yes".
physically equivalent