That's a great question.
Even though you are not escrowing your taxes with your mortgage lender, your lender requires that you verify payment of the real estate taxes.
Your mortgage lender also requires a loan policy of title insurance without exception for real estate taxes. The title insurer will check to see if there are any real estate taxes currently due and payable. Currently due and payable means that a bill has been issued by the tax office. Even if the bill says you are in the discount period, the taxes are still currently due and payable so the title insurer must collect these taxes from you and remit them to the tax authority in order to issue a clear loan policy to your lender.
This is why you have to pay real estate taxes at closing even if you do not escrow. It sets the slate clean and from that point on your responsibility is to pay your taxes as they come due and provide proof of payment to the lender annually. If you fail to pay your taxes, most mortgage lenders will revoke the waiver of escrow, step in and pay the taxes to protect their security interest. They will then setup an escrow account for you and if you fail to fund it, start foreclosure.
I've been in this business for a darn long time and it is my observation that most consumers get into trouble without an escrow account. This is why responsible lenders view the waiver of escrow as a privilege and they only grant it to consumers who have demonstrated an ability to handle it or have a large equity position.
Since we are on the subject of waiver of escrow, I think it's important to note that a failure to escrow taxes by the predator mortgage lenders who engaged in the subprime market was a primary cause of the property value bubble. They setup consumers who were irresponsible with money - needed subprime lending - and left them with paying taxes on their own. Do you think they didn't know consumers who have a hard time controlling their finances wouldn't pay their taxes? Of course, they knew. Once the consumers got tax sale notices they needed to refinance again to save the house and all the lender had to do was up the value of the property to cover a new mortgage and then set them up yet again for another failure with another escrow waiver. This was a churning scheme with each transaction pulling in thousands of dollars for the subprime lenders and ballooning values to cover the new fees and all based primarily on a system of NOT escrowing property taxes. It was hideous but I am rambling and I think I have already answered your question so I'll stop here. ;)