When I lived in Indonesia I met a housewife who told me she learned English entirely through diligent application of this method, no formal language education. She told me that I was one of only a few native English speakers she'd spoken to about it (she was really shy about her English, I think the only reason she spoke to me because I spoke fairly poor Indonesian in return!)
For my part, I would have happily believed that she spent 2-3 years living and studying an English speaking country.
She might have been lying to me, but it didn't seem like it at the time. All the information is there if you take the time to really study and memorise it.
I find it hard to believe that anybody could just accidentally pick up English from TV, but maybe that's where the "diligent application" comes in. On a related note, I think Indonesians might have an advantage over speakers of many other Asian languages when it comes to learning English. The Indonesian standard vocabulary has (IIRC) 10 or 12 thousand words borrowed from Dutch and the language uses a Latin alphabet.
Another advantage is that nearly everyone in Indonesia speaks at least two languages, Indonesian being a second language to whatever local language is spoken in your home region.
You're certainly correct about the alphabet though. In my experience, another big challenge for Indonesian speakers of English is correct grammar - Malay-style grammar is quite simple and usage conforms pretty well to its few rules. Although that applies to most people learning English as a second language.
Indonesian has also picked up many new or specific terms from English. I got in trouble with my history professor because I couldn't pronounce "historiography" correctly as "historografi".
(EDIT: Ok, this one might via Dutch. Recently terminology pretty much always come from English, though.)
It seemed from my brief exposure to Indonesian that it uses a very similar set of phonemes to English, which might be another advantage. Not having actually studied the language I can't say for sure.
For my part, I would have happily believed that she spent 2-3 years living and studying an English speaking country.
She might have been lying to me, but it didn't seem like it at the time. All the information is there if you take the time to really study and memorise it.