I'm assuming by "recognized" you mean accepted as a license suitable for exchange for a local license (in other words, to skip the learner license process and some tests).
Whether a foreign license is recognized for exchange or not depends on the state, and on the foreign country involved. Each state has different reciprocal agreements (usually none at all). So for some states it will be routine to accept a particular foreign license, for most others not possible, there isn't really much of a grey area.
For example California doesn't recognize foreign licenses: if you have a license from another country, you will be required to take a driving test. Same for New York (unless the license is Canadian). Some states may require tests even if you have another US license (it's usually at their discretion).
South Carolina does waive the knowledge and skills testing for those with valid licenses from France, Germany and some US territories (but not Canada). Texas doesn't require the tests if you have a license from Canada, France, Germany, South Korea, or the US or US territories.
It's unlikely whether the state accepts the license for exchange or not would make any difference to the insurance.