The value depends entirely on volume, which is why the honest answer for most first year businesses is no. A business receiving a handful of enquiries a week does not have a coverage problem, and the effort of configuring something to answer questions well exceeds the effort of answering them personally, which also produces a better answer.
The failure mode is worse than the absence. Somebody who opens a chat, types a question, and receives nothing has had a worse experience than somebody who found a phone number and used it. They also frequently do not try again through another channel, and you never learn it happened because there is no record of a conversation that did not occur.
Where it genuinely earns its place is a recognisable set of situations. High volume of repetitive questions with definite answers, such as hours, location, availability, or the status of an order. Coverage outside working hours where the alternative is silence until Monday. Or qualification, where a few questions route somebody to the right place before a person becomes involved.
The cheaper alternative that solves most of it is a well built page answering your most common questions, linked prominently. It handles the same repetitive queries, costs nothing to run, requires no configuration, and has the additional benefit of being findable in search, which a chat conversation is not.
If you do install one, make escaping to a person immediate and obvious rather than buried behind several attempts. The measure of a good implementation for a small business is how quickly somebody who needs a human gets one, not how many conversations were handled without escalation.
Set the expectation honestly in the greeting. A widget saying somebody typically replies within a few hours during business hours is useful. One implying live availability when there is none converts a helpful tool into a broken promise, and the visitor blames the business rather than the software.
There is a newer consideration worth stating. Tools that generate answers from your own content can produce fluent responses that are confidently wrong, including about your prices, your availability, and what you offer. A wrong answer given in your name is a commitment somebody may reasonably rely on, and constraining what it may say matters considerably more than how well it converses.
Then read the transcripts weekly for the first month rather than only the volume. What people actually type reveals both the questions your site fails to answer and the moments where the automated reply frustrated somebody, and both are more useful than any completion metric. Most businesses install one and never read a conversation, which means they learn nothing from the thing they installed to learn from.
Check what it does to page speed before installing, since third party widgets add requests and some of them load a substantial amount of code on every page. A tool that slows the site for every visitor in order to serve the small proportion who use it is a poor trade, and the effect is worth measuring rather than assuming.
Consider whether the same effort spent on response time would produce more, since a business that replies to email within the hour has solved the underlying problem without adding anything to the page. The widget addresses immediacy, and immediacy is achievable through a notification on your phone.
Remove it if the volume does not justify it rather than leaving it running out of inertia. A widget receiving two conversations a month is an ongoing cost in page weight and attention for a return that a contact form already provides.