I don't think it would be misleading. It would something similar to the Phrase from the CSRs end to the customer. Both the CSR and the customer will see it as part of the chat and both will be aware of it.
Instead of sending email survey, it would be a URL added at the end automatically on the CSR behalf. it is not necessary that it gets included in the transcript log attachment if that is misleading but the idea is that the customer gets a survey URL link at the end to take a survey.