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Yes, it can if the operating agreement is structured correctly (and you would need to see a local tax attorney for assistance in that regard) and if you can justify paying yourself less than what your business makes. In other words, and in regard to the latter requirement, you would need to be able to prove (if the IRS questions it) that paying yourself $50,000 per year (as an example) is reasonable compensation for the services rendered and that the remaining $70,000 of profit (as an example) is pure business profit and may pass through to you as an owner, not as an employee.
Then you only have to pay self-employment taxes on the $50,000 and not the whole $120,000.
Then you shouldn't have any issues. The LLC is not what really matters -- it's that your LLC must be taxed as an S-corp. An s-corp cannot have a non-resident alien member.
Here is some more information on your initial questions re the tax savings for an LLC taxed as an S-corp: