According to a 2005 study by Thierry Devos and Mahzarin R. Banaji, yes, at least for Whites and Asians.
Here’s the abstract:
Six studies investigated the extent to which American ethnic groups (African, Asian, and White) are associated with the category “American.” Although strong explicit commitments to egalitarian principles were expressed in Study 1, Studies 2–6 consistently revealed that both African and Asian Americans as groups are less associated with the national category “American” than are White Americans. Under some circumstances, a dissociation between mean levels of explicit beliefs and implicit responses emerged such that an ethnic minority was explicitly regarded to be more American than were White Americans, but implicit measures showed the reverse pattern (Studies 3 and 4). In addition, Asian American participants themselves showed the American White effect, although African Americans did not (Study 5). The American White association was positively correlated with the strength of national identity in White Americans. Together, these studies provide evidence that to be American is implicitly synonymous with being White.