Yes the pi will indeed slow down and can possibly even shut off when the cpu overheats. Because of this in built thermal throttling functionality you should not be able to damage a pi by running it continuously.
On a side note you do realize that the pi draws a similar amount of power as a cellphone and has a cpu designed by the same company that makes cellphone cpus, and not many phones have heat sinks, let alone ones that are as large as the one you are using. It has been a long time since I have seen a phone user not run their phone 24/7/365.
