Yes this sort of logic will work. In your load script you can write the logic using an if statement. I created a small example below. The exact expression will depend on how you want to deal with other members in the RegionA or RegionB fields. If you have a more complex logic (e.g. different outcomes for RegionC based on several combinations of RegionA and RegionB you may want to concatenate the two fields and then use a mapping table to resolve the logic.
If(RegionA='ASIA' or RegionB='ASIA', 'ASIA', RegionA) as RegionC,
Depends on the data model and what you want to achieve. If the new field is supposed to be in a table which already has RegionA and RegionB, then sure. If RegionA and RegionB are in different tables in the data model, then no, unless you match them in some way.
If it's just about Asia, then no problem. As already suggested, create new field in script like this:
If(RegionA='ASIA' or RegionB='ASIA', 'ASIA', <whatever it's to be when neither is ASIA>) as RegionC
But you can't store "logic" in a field, just the result of applying it to other fields. So, if you wanted to switch to selecting "RegionA='UK' OR RegionB='UK'" at a click, you can't do this that way. For that you have to either incorporate set analysis into your expression, or create the new field as linked to all combinations of RegionA and RegionB which satisfy the logic for each and every region. I'd stick with set analysis if I were you.