I don't know what Vedic Astrology is per se. However, from what I've read and heard about Astrology there are really two levels: the frivolous, for example, the sorts of Sun Sign forecasts you read in daily newspapers and magazines, which give very vague and general information. As the world population is divided into twelve calendar months, it's not very difficult to realize that four billion people divided by twelve, you're going to have millions all having roughly the same thing happening to them. This, of course, is rubbish.
Then we have the more serious level of Astrology whereby the time (right to the minute) and the place, (right to the square mile or so) give the Astrolger a chance to look up his or her chart records (which, apparently date back millenia and have been, in theory at least, tested against hundreds of thousands of cases) so they can make an Astrological Chart for this particular person.
What comes into play here is not only the general 'Sun Sign) that is, the area of sky above the point of the place where the person was born, but also the phase of the moon at that time and the angles of all the major planets relative to that point on the earth's surface. So it is a matter of precise angles.
These angles represent the intensity of the radiation coming in (that is emanated by or perhaps reflecte by) the planets on this particular patch of earth at the time the child was born. All pretty 'scientific.'
Where it could well fall down is in the 'interpretation' of the Astrological Chart by the Astrologer who made it up. There is a helluva lot of subjectivity comes in here. So, to answer the question - and referring to the only type of Astrology i've heard about - it is "sort of scientific."
Hope that helps.