Not very likely. With other countries (like Japan) there is more government-to-government sharing of information, but Taiwan is in this weird diplomatic situation, and the amount of money involved probably isn't worth chasing.
Even if the government there and here opened up all their records to one another, and the U.S. was willing to surmount the language problem, a basic difficulty is that the U.S. system is based on the SS number--which nobody here will ever ask for (except U.S. banks, which are required to do so by law). And it's no good trying to track people according to passport numbers, because those change, and anyway are not cross-listed with SS numbers very well. (Remember, a lot of people don't HAVE an SS number, especially if they are very young, or haven't spent much time in the U.S..)
The IRS can still catch you, however, if your spending patterns back home fail to tally with your ostensible lack of income. They catch a lot of people that way.
Oh, one more thing: although you are required to file U.S. taxes, you shouldn't owe anything unless you make more than about USD 80,000 a year. That's because the U.S. and Taiwan have a tax agreement designed to prevent double-taxation, and the U.S. excludes this amount. Of course, they might still say you owe something--and then what are you going to do, fly to DC to appeal it? (They routinely do this for amounts of under USD 500, because any higher and it triggers some kind of automatic review.) Also, some states may consider you their resident for the purpose of assessing state income taxes.