Can the Heym Express bolt action rifle chambered in 600 NE be re-chambered to 600 Overkill?

Certainly, however you must ensure that the bolt head will engage the base of the 600 Overkill cartridge and that this round will work with the magazine. My recommendation would be to contact American Hunting Rifles and determine what the parent case of the 600 Overkill actually is and compare it with the 600 NE. In my estimation I would belief the best action would be to leave it as a 600 NE as AHR (a great company) may not be around in say 10 years that being the case you would have a very hard time finding brass. The 600 NE however belongs to Holland and Holland who are not likely to pass into oblivion any time soon and the 600 NE has been around and is popular enough to enable you to find brass at the minimum. Keep it a 600 NE and I think you will be better in the long run. Performance of either is enough for anything on this planet!