Not talking directly about legal status, just about potentially losing the green card! If you want to keep that you will need to be present in the USA. If you want to work in the country as a pilot you will almost certainly require FAA certificates (may be exceptions if you are flying internationally on foreign registered airplane).
It would be nice if employers would guarantee employment if you got x type rating or whatever qualification but thats unlikely to happen. You will have to fork out for the ATP and THEN apply. As was said above, in the scheme of things its not that big a deal.
As for employment, which is what you asked about, who knows until you apply. There are not that many 737 operators in the USA and dont forget smaller ones such as Miami. The job market is better than it was at the time of your first posting but walking right into a command position may not happen. Dont forget to keep us posted on your progress