No, you don't know when the threshold has been reached unless you encode it into your share's format.
To understand this, I'll quickly revise how SSS works:
The person to share a secret constructs / chooses a random (large) prime and chooses $k$ random numbers (the coefficients), where $k$ is the threshold. From the coefficients he constructs a polynomial. For each share, he picks a random $x$ and evaluates the polynomial of the $x$ to receivce a random $y$ in return. A pure share is just the pair $(x,y)$.
Obviously, you can't learn the degree of the polynomial from a bunch of (random) points so there's no way to recover the threshold (which is the degree + 1). You can however define a format for your shares that includes a) the prime generating the needed field, b) the threshold, c) the $x$ value of your share and d) the $y$ value of your share. In this case you can recover the threshold from your shares.
Is it possible to determine if a share is a "valid" share?
As explained above, a share is (maybe) some general parameters (threshold, prime) and a point. As the x-coordinate of the point should be completely random, the y-coordinate will also be random and so there's always a polynomial going through that point.