If you are thinking of a regression, or similar, to predict level of higher education reached, then yes you can, unless I am misunderstanding what you are asking [which is always possible :-) ]
But what tends to happen (in my experience, anyway, using the Q software - whether this also happens with Latent Gold I have no idea) is that the segments found using Latent Class sometimes differ more on the constant term in the regression, and less on the coefficients.