No. Timeout will only happen if an active user session is available, but there are other flows running and the current flow is in queue for 3 hours or more (that's the limit for a queued desktop flow).
You should make the email get sent when it fails. If there is no active user session available, the action will not timeout, but it will in fact throw an error and fail right away.
Normally, if that happens and the cloud flow is running on your own account, you should already receive an automated email from Power Automate, saying that your flow failed. You only need to set up extra emails, if the flow is running on some other account, like a service account.
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