Nope. Фон means "background". It is also a linguistic term unknown by most native speakers.
Since you, probably, did not know that meaning of "phone" in English, I think it is safe to assume you won't need it in Russian. "Background" is useful, though—just not in the historical sense. It is more like a literal background or something that figuratively serves as a background against which something else happens.
So, if I were to ask if someone had a phone in AE, most people would assume/know I was asking about a landline telephone. Where as if I needed to ask if someone had a mobile phone, I'd use the word "cell", or (in some dialects) a "mobile".
What, if any, correlation exists in Russian? If I ask for a телефон, would I be directed to the nearest landline?