I used to be a line engineering manager at Cisco before I left. Sometimes, during an LR, HR recruiters would reach out to me with an internal candidate who they thought might be close to a fit but was facing an LR. I always gave them a shot and even hired a few. I know at least a couple of my peers had the same perspective.
Sometimes, these candidates surfaced because their managers reached out to HR and advocated on their behalf. (in other words, you should use your network)
So Its totally possible to get a job during the 30 day period. However, its not substantially easier than finding a job elsewhere. I guess it can be slightly easier to get an interview, but you still have to be a fit for the job and show well in the interview. I would fully expect the hiring manager to reach out to people in your org for references ... something to keep in mind.