Can "work" be a countable noun?
It can be...
Excluding art and literature ("The works of Shakespeare"), we normally use "work" as a non-count noun. But in archaic English, we sometimes see it used. Percy Bysshe Shelley's most famous poem, "Ozymandias," contains the famous phrase "Look upon my works, ye mighty, and weep!" Catholic and Protestant theologians have debated for centuries about the significance of "good works" in regards to personal salvation.
More recently, most big cities distribute natural gas through a "gas works." The US Army's top research and development labs in the 1940s were housed in a complex jokingly referred to as the "Skunk Works." And when I buy a hamburger? I get it with... the works!