Sure, anything is possible. :D But unless you listen to full blown on conversational tagalog for about 3-4 months everyday and converse with people who will teach you the language I think your going to lose your shirt on this one. Filipinos can be biased when it comes to language. They listen and will now which dialect you are speaking and what part of the country you are from so it'll be hard to get past your lady.

As an example, I grew up listening to Cebuano but never really had the need to pick it up. When the time came and I decided to learn I had my parents speak to me only in Cebuano. I also had a tourists guide book that I thought would help me to speak Cebuano. The result after 7-8 months I could speak some but it wasn't right. One thing that I found out was that the conversational Cebuano my parents used was from the 70s and people in the 90's didn't use some of the words anymore. ex. Ginakanin (parents) was something that Cebuano's don't often use anymore. I guess it'd be like talking to someone using words like "Groovie" and "Far Out Man." Sure you can use it but it just doesn't fit the times. Also new words had come about like Bisdak - Bisaya Dako (sp?). I asked my parents what it meant and they had no clue. The hardest thing is that when I do speak Cebuano I think in English first. I believe if you can get to the point where you think in the language you want to speak you've got it made.

From my experience to be able to speak without an American accent would be possible by using total immersion. i.e. live in the Philippines for 6 months or so and speak the language and listen to people and you should be able to shake the American accent.