In short, no.
American Sign Language (ASL) is not a universal language. There are over 400 signed languages used worldwide, just as there are multiple spoken languages. ASL is considered to be the native language of Deaf people in the United States, and is recognized in other areas such as Botswana where ASL was the first exposure to a full signed language.
There are many Deaf people who rely on speaking and speechreading, never learning ASL (or the signed language of their country). These are trained under the belief that since oral communication is most common, it would be the best choice for conducting life and business as an adult. Advances in hearing aid and cochlear implant technology provide support and momentum for this idea. A variety of factors, including social and economic networks, nudge many orally trained people toward learning ASL as adults while others find a comfortable level of success with oral communication.
There are also late-deafened adults who already have a language base in written and spoken English (or the common language of their country). These are more comfortable with captioning and written notes for clear communication. The effort required for them and their families to learn sign language outweighs the value of using resources they already have to communicate. Some of these learn sign language and embrace deaf culture, at which point they have two worlds to operate in.
Outside the U.S., especially in less developed countries, there are Deaf people who do not have a language. It’s not that no language exists, but rather that these people are kept in the shadows, considered to be lesser people without the ability to participate meaningfully in their homes or communities. Some are simply neglected while others are actively abused. The good news is, ministries and educational organizations are stepping up to provide language, education, and skills to Deaf people in these places, providing a new hope and future.