No, a neutral accent is usually called a "Mid-Atlantic accent" because it is between American and British accents. Certainly it is not the accent of the USA, which has dozens of different accents, many of them very strong (e.g., the South, New York, New England). It would be closer to a Canadian accent (although without the diphthongs that make "about" sound like the Canadian "aboot"). It isn't necessary to learn any particular accent: rather, it is necessary that you don't speak English with a strong accent of your own. For example, Russians tend to pronounce the vowel "i" as "eeee" (making "ship" sound like "sheep"). Softening this accent so your English is more understandable to a native speaker is the important thing, not sounding like a Brit, a Canadian or an American, which would be impossible anyway.

Your own accent will be fine.

Neutral accent is a way of speaking a language without regionalism. Speaking with an accent affects our communication and sometimes at its worst spoils our image in public. To make ourselves understand better we should speak in neutral accent. Ref: http://www.neutralaccent.com