Not according to the data. There is absolutely no period where general college attainment has shown to improve mobility when as compared to equivalent people without college attainment.
What the data does show is a tendency for those with the capability to successfully complete college to have greater mobility when as compared to dissimilar people (i.e. those hindered by disabilities), but it is faulty to attribute that to college. Clearly it is the life challenges that hold people back. It is not the lack of a degree that keeps the down syndrome kid from being considered 'management material'.
There is a stronger case to be made for high school attainment, but even that is no doubt confounded by the rise of industrialization showing up at the same time, providing new mobility opportunities. The meaningful gains in high school attainment we have seen over the last 20 years have not translated to improved mobility for that subset of the population.