Is there a limit to how long the pause action can handle before timing out?
I.e. if I try to pause for 365 days, will the workflow timeout or actually pause for that long?
There is no official article mentions that there is a limit for workflow pause action. Per my knowledge, it is ok if you pause for 365 days. The pause action will not cause the timeout issue.
In SharePoint, workflow limits are:
For more information about Workflow limits, read the following article: