If it's on a different domain and servers, I don't think it will be an issue.

If they have it on an API call to (making it up) api.slack.com/status it might very well go down when things go wrong, making it useless.

However if they physically host it elsewhere ideally on a different cloud provider, with a different domain, say, slackstatus.com/api-status that is completely separate from the actual services, which can both query the actual service with a call from outside and can be updated manually with physical persons at Slack, and the client checks that domain, I think it can work.