Looking for a state without going thru all the documentation or requirement process or not having a valid SS# that's work authorized is just step 1 of 2. Getting the ATT without the proper SS# is within this first step.
Here's number 2: in any case, if you're allowed to take possession of the nursing license, one will ALWAYS need either that (a). working approved SS# or (b). a working visa of some sort to work legally in a hospital or any legitimate US employer, whether it's a nursing home, any hospital job or a McDonald's.
At the same time, the license in your hands must be valid to work in that state and if you need to endorse it over to another state that does require putting a valid SS# on the endorsement application, if it's not on the application form, it will be not only rejected, but don't expect to get a refund for the denial, as most application forms clearly state to some extent..."NOT REFUNDABLE", some applications have them in BOLD letters, some have them combined with RED letterings.
As once that state's BON touches and opens the application, they will assume that you still at some point in time will be able to provide the missing valid SS# and usually give you 1-2-3 or so many years to "complete" your application. The clock starts ticking from that date.
Don't count on getting hospital sponsorships unless you have at least a couple of years of paid working hospital experience and helps more if your paid experience is in a speciality field. There will be some exceptions to this general rule, but don't count on that either.
Sponsorships are very costly to hospitals as they must pay for the entire cost and no need to spend more money for them when they can draw from a large pool of other qualified applicants (usually local US or residents) and can start the next day or within 1-2 weeks.
But to answer your question, at this present time, NY and TX will allow the NCLEX to happen without having a SS#, if your friend is willing to work in either states.
This could change at any time, as there were hundreds if not thousands that were caught off-guard when CA suddenly started to enforce the SS# on the application back in April 2010. Of which many who did pass the NCLEX in CA prior to April 2010 but didn't have the proper SS#, who then found out they don't have a license at all. Until the SS# is provided, then the actual license is issued and then one is truly an RN. This also applied to those trying to renew their license for the first time.
But you need to ask her how she plans to get the proper working SS# or visa to look for a job, no hospital or employer will take the chance to hire someone not authorized to work in the States.
I mean there might be some greedy employers that might hire under some undesirable conditions, such as crime ridden areas where even during the day time it's dangerous and they assign her only the night shifts. They might offer very high patient to nurse ratio with high demands, then puts your nursing license in jeopardy. The chances to be taken advantage of is high. They may offer less wages, no benefits, no vacation days, no time-off or if they do, it may be unpaid.