By default, assuming GPT-4/3.5 (the models used by ChatGPT) won't have been trained on your manuals, the models won't be able to provide useful information beyond what can be guessed by context of the prompt.
To make the models useful you'd likely have to set up document retrieval. A vector database would store embeddings for chunks of your technical documentation, pre-computed with OpenAI's embedding API. When a user asks a support question, you'd look-up relevant documentation by closest embedding similarity, then provide this as context to the LLM as part of the prompt. In implementing this, you may face challenges in data collation and the infrastructure involved.
Even with this, the model may struggle on tasks that require wider background knowledge of your products that can't be inferred from a limited number of chunks. For local models fine-tuning would be an option here, but that's not possible for GPT-3.5/4.
LLMs are known to "hallucinate" and give incorrect but confident-sounding responses. Moreover, even telling the model "don't answer if you don't know" won't necessarily prevent this, as LLMs lack sufficient introspection ability to know what they don't know.
Stating specifically what the LLM should stick to, such as only the content contained in the retrieved document chunk, should be more effective - but still won't entirely prevent hallucination. You could have the model provide documentation references for the user to check manually to verify accuracy.
In general, you'd likely have to work towards setting user expectations correctly not to expect the model to be entirely accurate.
Depending on how your support bot is exposed, you may have to handle misuse of the model by users. Paying for API usage could become costly if many users begin using it for long conversations unrelated to your product.
For example, after Slack's implementation of Claude, tools and tutorials popped up for using Claude for free, involving creating a Slack workspace as an intermediary.
Most likely you'd want to implement this using OpenAI's API. However, if you did in some way use the ChatGPT website/app, you'd also face the issue of data confidentiality for your gated documentation and user requests. For example, a user seeking support may copy-paste in a debug log containing IPs and names. By defualt ChatGPT trains on user input, whereas the OpenAI API accessing the same models does not.