It's not a matter of "accepting" a licence, it is what registration that is on the side of the aircraft that matters.
If you want to fly an N reg - you must have a FAA licence. UK reg - you must have a UK licence, VH reg - you must have an Aussie licence, etc.
That being said, some (alot of) countries will "validate" your ICAO licence that allows you to fly an aircraft with that country's registration. Most validations will have specific conditions attached to it. eg. You can only conduct aerial work and only for a specific operator on a specific aircraft type. These validations will also have a time limit applied (12 months in the UK).
Depending on where you want to fly and for how long will dictate if you validate your licence or convert your licence.
