hands_on123
If you intend to use a J1 visa to the maximum then the gaining of a CFII will help that goal as it will help you gain your first job faster. Plus it helps you gain more hours as you will be the instructor available to teach basic IFR instruction, as required, during FAA Commercial training.
It will also help you in the future when you decide to do the JAA instrument as you will have various dispensations for already holding an ICAO instrument.
If someone could give a constructive alternative in the US to instructing for your first job I'm sure most would head in that direction. Unfortunately there isn't!!