The most widely-spoken languages are Tagalog-based Filipino and English (the result of a U.S. colonial presence from 1898-1946 and continued close political, economic, migratory, and military ties with the U.S. since 1946). And, in the U.S. Census, Filipinos are included as a separate, Asian American category.
So for people for whom these criteria are most important, and who choose to define Filipino identity by the country’s evolution during the 20th century, the answer would be “no.”
On the other hand, a different definition of “Hispanic” could yield a different answer. Filipinos can be considered Hispanic if one prioritizes the definition that countries colonized by Spain are “Hispanic” because of that historical influence — no matter what their location on the globe or current linguistic status.
Spain colonized the Philippines in 1565 and ruled most of the country until 1898 (333 years) — a longer time period than in some Latin American countries. To research Philippine history during those 333 years, knowledge of Spanish is essential for scholars.
Ethnically, although there was not as much migration to the Philippines from Spain as there was to Latin America, quite a few Filipinos can claim some Spanish ancestry.
Migration to the Philippines from Spain was quite extensive after the Suez Canalopened in 1869. By this definition Filipinos could choose to self-identify as Hispanic.
Even today, the Philippines nationally continues to exhibit numerous traits inherited from Spain: overwhelmingly Roman Catholic religion and related cultural legacies, many Spanish personal names, Spanish musical traditions, many Spanish vocabulary words incorporated into Filipino indigenous languages, etc. People emphasizing this historical and cultural legacy could answer “yes,” Filipinos are Hispanic.
Finally, people could acknowledge the complexity of Filipino history and say “yes and no” — claiming some Hispanic heritage but recognizing that in the Philippines at least, it is receding as time goes by.