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Yes, and on Messenger there are two different handovers, which is worth understanding because they solve different problems.
Hand over to the Facebook Page Inbox. This passes thread control to Meta, so a teammate takes over in Facebook's own inbox and the bot stays quiet until Meta hands control back. Use it when your team already works in the Page Inbox. This one is Messenger only: it relies on Meta's handover protocol, which does not exist on other channels.
Hand over inside ChatinFlow. Set the conversation status, assign it to a teammate, and notify them. The bot stops because the conversation is no longer in an automated state, and the reply happens in the ChatinFlow Inbox. This works on every channel.
Most teams should use the second one, because it keeps one inbox rather than two. Pick the first only if your support team genuinely lives in Facebook.
Either way, the handover step is not the hard part. The hard part is the gap: the contact just asked for a person and nobody is there yet. Say so. A single line that sets the expectation, then the assignment, then silence, reads far better than an automation that keeps talking while a human is being fetched.