I don't believe you may fly around with a log book, secondly the logbook is neither a license, merely a record.
I also believe that you may not add a new type to a validation. A validation is only a copy/mirror of the original. Any new types that are to be added to a validation, must first be found on the original.
Imagine trying to produce a license without a type rating endorsement during a ramp check in Algeria, let's say, and explaining that it's in your log book with a signiture, is in another country, say Tunisia (example, where one could be based). I think you would be grounded and taken away.
Best bet, SACAA, Claudia, will know even better.