The short answer is yes. One can learn to speak tagalog with an undetectable accent, but I would guess that it is not commonly achieved by kanos. My answer is derived from the fact that I, an American, have developed a nearly undetectable mexican accent, with my spanish. So I would geuss that it is possible, but like with every talent each person has a different level. Tagalog for me is a much more difficult accent to develop, but I have been around mexicans (I live in California) far more than I have been around filipinos. I have noticed that with the little tagalog and bisaya I have learned, the more I hear a native filipino/a speak it, the better my accent gets.

How long it takes for you to be able to hold a general conversation depends on your affinity to learn Tagalog, and how immersed you are in the language. Difficult question to answer without those details.

Brian