Are there any downsides to not following the publication requirements? From my research the only limitation (which wasn't even conclusive) was the ability to sue may be hampered until such a time that you comply with the publication requirement.
The law goes all bogeyman here, but one thing is clear: If you get busted for not publishing, you are no longer in good standing as an LLC in the state of New York. You then have to publish to get back in good standing.
This doesn't affect the terms your past or current contracts, but it does mean that you can't take contracts with government agencies and some potential clients will research your company and see that you're non-compliant. This can lead to a loss of business and the terms of most of contracts (that I've come across, at least) stipulate that you must be a valid LLC in good-standing -- if you go ahead and sign that contract, you're operating counter to the terms that you've entered into and may be liable for damages to the other party (or your actions could invalidate their responsibilities to you). Note that severability clauses do not cover you in this instance because publication is a legal requirement of the state.
And you're right -- you can't sue others as an LLC or fully defend your contracts in a court of law while behind on your liabilities.
You're also not technically supposed to do business while non-compliant.
disclaimer: not a lawyer, but it's not my first time at the rodeo and this stuff isn't that complex
