If they really wanted, Famous Company has a lot of money. They could buy citizenship for me and my girlfriend at a cost of $250,000 USD each. Then I'd be able to work for them anywhere.
These parameters are personal though, not job-interview criteria. It's about relationships, friendships, trust, and life goals. "Networking", in the social sense.
But if Famous Company doesn't want me to tell my boss, I feel like they don't respect that social network. I'm committed to being a good boyfriend, employee, and foreign resident.
I'd like to make friends with the person from the Famous Company, and build a connection with them too! Maybe stay longer in Taiwan to work for the Famous Company in 2019, or apply for their jobs in another country. I just don't want those communications to disrespect my existing commitments.
The main problem seems to be ,should I tell my boss now... because he is your friend the only answer is yes. anything less will likely haunt you for years. Famous Company does not need to know who you told about their offer, so do not tell them. Tell the boss now, then go get the offer, with a solid offer in hand ask the girl what "we" should do, then ask boss what he thinks. I'm sure that whatever advice they give will be better than anything else you will find.