I got added to my hubbys bank account without SSN no problem.....the bank personnel photocopied my passport containing my visa/I-94 filled in and signed a W-8. I was issued a debit card with no problems!
Once i have a SSN i just need to inform the bank who then will update my info on hubbys account!
I have heard that some banks wont do this though without an SSN.....before we moved to Nebraska (my hubbys bank in NC) were oblivious to the fact that indeed i could be added to his account w/out one until they actually phoned they "head office and enquired about it" to their embarrassement i was right and they were wrong........i did however receive an apology

after months of them saying NO its not their policy to add people to checking accounts without SSN's.
If a bank tells you NO they can not add you to your spouse's checking account then theyre mistaken, all they need to do is fill out a W-8.