Over the years, employers have developed policies and procedures such as requiring employees to sign arbitration, and these types of agreements as a continuation of employment. The short answer is yes, an employer can require you to sign additional requirements and agreements IF YOU WANT TO CONTINUE TO WORK at the company. I put that in all caps because clients often forget this one major rule- you are not forced to continue to work somewhere if it is not to your benefit. If you have other opportunities for work in the short term and signing these documents will hurt you, then you have a choice to leave the company and not sign the documents. But, if you want to continue to work at the company, your employer has the right to force you to sign these documents, and the consideration for you signing these documents, is that you get to keep your job.
As Mr. Celler states so well, NO, you are not obligated to sign it. And if you do not, your employer thereafter will NOT be obligated to keep you as an employee. The length of your employment is unfortunately irrelevant.
This response is not legal advise.