Meaning of "Always On" setting on Azure Web Site

Yes both will be prevented when you have "Always On" turned on. The answer to the question you linked to (Will "Always On" setting prevent BOTH idleTimeout and periodicRestart?) contains the full details. If you have multiple instances running "Always On" will also ensure that all of them stay running.

For long running processes I'd highly recommend using Azure Web Jobs if you can. The Azure Webjobs SDK will make your development life a lot easier and provide you with a lot of nice monitoring for free. Check out this tutorial by Scott Hanselman here: http://www.hanselman.com/blog/IntroducingWindowsAzureWebJobs.aspx

FYI, Webjobs run in the context of your website, so if your website is recycled (if Always On is disabled) then your Webjob will also stop running. Enabling "Always On" will keep both your web jobs and your web site up.

From Microsoft Azure How to configure websites

Always On - By default, websites are unloaded if they have been idle for some period of time. This lets the system conserve resources. You can enable the Always On setting for a site in Standard mode if the site needs to be loaded all the time. Because continuous web jobs may not run reliably if Always On is disabled, you should enable Always On when you have continuous web jobs running on the site.

If you have things that need to be running continuously you could look at either Azure Webjobs or Worker Roles which would be more reliable rather than IIS threads.