You should begin to see statistics update essentially immediately, though not all will be updated in that time frame. The Job Scheduler will ensure that the polling jobs are evenly distributed over time to prevent the Orion server from becoming overwhelmed. If the server has been backed up or offline for an extended period of time this can take anywhere from a few minutes to catch up, to 2-3 polling cycles depending upon how much is being monitored and how many different Orion products are collecting data.
Data is written to the database in near real-time as it is collected. There is a queue, but it should be emptied virtually immediately if the database is online and functioning properly from a performance perspective.