This subject has been covered in previous threads. I'd recommend that you search for more info via the search function at the bottom of the forum page.

Rough summary of some thoughts...
Some varieties will tend to root above the graft in these situations, some will not.
Performance may depend on factors such as varieties involved, nature of soil, environmental/cultural conditions, etc.
If the scion does root, you will loose all the possible advantages of the rootstock.
Crown and root rots are a possibility.
Trees already on standard (full size) rootstock are generally available.

One interesting possibility of getting trees to self root that was discussed on a NAFEX thread was the idea of planting the graft union just above the soil line and waiting for the tree to come into full productivity before raising the soil level and allowing self-rooting. The fruiting itself would tend to reduce vigor but the tree's more vigorous root-system might be advantageous in terms of anchorage and ability to withstand drought. Some people would like the idea of growing larger trees if they could just harvest fruit sooner and this strategy might create a best of both worlds situation.

A trees ability to self-root is generally not very well studied cultivar to cultivar as B7 suggests. On the above mentioned thread the cultivar being proposed was Northern Spy, which is well known to easily self-root. Mostly the literature indicates that self-rooting is quite common when exposed to soil.

A self-rooted tree would also undoubtedly behave differently depending on soil and climate. In adverse environmental conditions such as limited moisture, short growing season, and shallow soil, any rootstock will have less vigor.