Yeah, it's a word. Dictionary.com lists "phone" as a verb as well as a noun, meaning that its present participle and gerund forms are also possible. It's not a good translation, however, because "phoning" indicates the act of using a phone, while the Korean only indicates that phones themselves are bad for you.
I think you're partly right. It depends on whether your going for the active participle, the act of calling, in which case no, or the gerund, the calling, in which case you have a point. 전화 can refer to a phone call as in a phone call came: 전화가 왔어요. The second hangeul means talking. A telephone conversation is 전화 대화 and it's the same 화 (話: 電話 對話) . . .
. . . but it also means the phone, though you can use 전화기 for the telephone set if you want to get technical . . .