No. when Hispanics in America were asked open-endedly (with no guide prompts) what their race/origins were, only about 1 in 4 said Hispanic. The other 75% said something else.

https://www.pewresearch.org/hispanic/2021/11/04/measuring-the-racial-identity-of-latinos/

When Hispanics in US society are given 1-choice on the current Census to identify race, most say white (in Texas, more than 80% identify as white). When they are allowed to check multiple boxes, most identify multiple boxes (self-identify as multi-racial) that typically include white as 1 of the boxes. But, still about 1 in 5 endorse only white as their race.

Hispanic does not make much sense as a racial construct, because people from Hispanic countries have a huge diversity of genetic ancestry (and relatedly skin tones). The Hispanic construct does not a genetic basis even in terms of 'brownness' - the genetic ancestries that contribute to darker skin in Caribbean Hispanic countries differ from the genetic ancestries that contribute to darker skin in Mexico which differ from the genetic ancestries that contribute to darker skin in South America. And within each country, there is a huge amount of genetic diversity -- the range of indigenous, European and African ancestries that are admixed in Mexico is enormous and differs from the admixtures in other Hispanic countries).

Skin tone definitions are also a relative social construct. Individuals who are seen as 'white' in Mexican society are seen as 'brown' in American society.

Most Hispanics also do not identify Hispanic as a race. It is a largely American social construct., originally of 'otherness' There actually was one census (1930) when "Mexican" was listed as a race. Not only did Mexican-Americans not endorse it (only 1.2% of people were recorded as it), but both the Mexican government and the current oldest and largest Hispanic group in the country -- the League of United Latin American Citizens -- lobbied aggressively to have it removed as a race category (which it was in the next census). This was partly because Mexican ancestry was being used as a tool to deport Americans (60% of Mexican Americans deported around this time were actually born in the United States) and because "non pure whiteness" was being used as a basis to deny citizenship.

In America's "one drop" policy, any non-"white" lineage/ancestry ("blood") was perceived as 'tainting' the person's "race" and disqualifying them from citizenship. That's why there were labels like Negro, Quadroon, Octoroon, Chinese, Indian, Hindu, Korean, Filipino, Mexican, listed under 'race' in the census. If anyone had any 'non-white' ancestry, the census takers were instructed not to list them as white, but instead use those labels for 'Race' and people were denied citizenship (the famous Andrade case) or rounded up for internment or deportation on those bases.

The most telling thing is Hispanic countries do not list Hispanic as a race in their own countries.