While the front bearings are most of the load that will be seen on the spindle, it's still worth the time and money to maintain the rear bearing as well. This is because it keeps the spindle steady (to an extent) at faster speeds, which provides rigidity.
If possible, I would try to make a mounting platform such that you maintain all bearings on the spindle. On a lathe, you want as little runoit as possible. As such, again, maintain the back bearing as long as possible until you know you cannot keep it. At that point re-think how you want to do it, as once you cut the end off, there is no going back.