Do phagocytes need antibodies to be able to engulf pathogens (to function)?
Phagocytes don't necessarily need antibodies to recognize intruders, i.e. by presence of non-self sugars. Additionally, phagocytes can aid amplification of effective anti-bodies by presenting degraded pathogens to the adaptive immune-system. I found this concise summary of the innate immune system, that I would strongly recommend to read!
Now to your more specific question: Detection of viruses. You have to consider, that viruses are highly optimized to evade the innate immune system:
Viruses can happily replicate and mutate without proof-reading without negative consequences and with relatively low conceptual constraints, as they are so simple, compared to cells. This is why the innate immune-system is prone to miss viruses (at least those, that are optimized for a certain species). Imagine how big of a genome you would need to cover all possible viral substances by at least 1 innate gene! Read about hyper-mutation to understand the role of antibodies to detect even these highly evasive viruses.