Is your driver's license or vehicle registration suspended due to a lapse in auto liability insurance coverage?
yes
You can provide proof that you now have insurance online or by mail.
Will the DMV verify my coverage with your insurance company?
the DMV will verify your coverage with your insurance company
By the way, if I want to get out of state insurance and keep my vehicle registered in New York, what could happen to my insurance coverage?
Your valid insurance coverage will lapse.
so, if I get a insurance for my vehicle in another state I may have troubles?
That's right. But you can send us a copy of this documents, to avoid any kind of sanction.
And what will happen if I don't send you that document?