Keep Intercom for the support record
Intercom should stay where your team reads the conversation, works the ticket, and sees the support history. That is the job the product already does well.
Intercom already exposes webhook and API access for conversation and ticket workflows. The useful question is what should happen because a conversation was created, a ticket changed, or a pattern in the queue started to matter.
Where support teams still lose time
The queue can show that a customer is frustrated, that the same account has opened three tickets in a week, or that a conversation now needs a different owner. It does not always finish the work around that moment.
Someone still has to escalate the issue, warn the account owner, update the CRM, flag churn risk, or make sure the next follow-up actually happens.
A practical way to use both
Keep Intercom as the place where support conversations and tickets live. Let Neudash react to the Intercom event that matters and handle the routing, alerting, reminder, or cross-team handoff that should follow.
That is usually where the value shows up: not in replacing the inbox, but in making sure important support signals turn into action.