Can I make up for under-proving my bread dough during the first rise by doing an extra long second rise?
No, you cannot and should not, as the first and second rises serve different purposes.

The first rise is mainly for developing gluten and flavour, and after pressing the air out the second rise allows the bread to be fluffy when baked without large air holes developed in the first rise. This is especially true with bread baked in a loaf as you specified, where relatively tight crumb (as opposed to that of a baguette) is usually desirable.  

So one issue that may arise is cracking on the sides where the dough rose as it was cooked, due to the lower amount of gluten development, but this should not affect the structure or taste of the final product. If you were to proof the bread too long in the second time, the bread may collapse in the oven, resulting in a dense loaf.