Getting the account is one thing ~ by the time FDIC is in the picture you need to identify yourself ~ again ~ and your status as an unlawful entrant will definitely be available for the gub'mnt to match up to ~ and there goes the big enchilada.
You literally risk being picked up by ICE for making your claim.
Could be, though the IRS could give a rip, and I’ll bet the Administration tells the FDIC to turn a blind eye just like they tell ICE.