Doug,
The response to your question " is it OK to do this (=add the PROCES ARITH(EXTEND) statement globally ) for all generated COBOL, or are there caveats? Don't want to introduce any problems if it can be avoided." is that you should not/must not use ARITH(EXTEND) for all Gen generated COBOL because the Gen runtimes will not be able to handle numbers larger than 18 digits.
If you want to call non-Gen code passing larger numbers, you can customize the interface to the external application (assume this is an EAB) to your needs but you must ensure that what is returned to Gen is within 18 digits or you will experience problems.
If you want to discuss specific requirements please open a support case.
Regards,
Teresa