Right.
There are two issues. 1. The preamp needs power to work, the power injector supplies that, and cable resistance might reduce the delivered power enough to cause the amp not to work. 2. The amplified signal is reduced by going through the cable, the longer the more loss, and there's always more loss at higher frequencies than at lower frequencies.

If you can put the power injector 100 feet from the antenna, any others further away will not do anything at all to help.

However, there's reality -- maybe it doesn't matter. Being the lazy type I am, I'd first try it 300 feet from the antenna to see if that works. Next, can you put it real near the antenna, say in the last 30 feet? I don't know the details of your setup so I can't do but ask.

The signals themselves are another matter. There are two reasons for an amp -- to amplify signals that just aren't strong enough from the antenna, and to amplify signals that the cable attenuates. A seat-of-the-pants approach, where you just amplify the whole mess and feed it through a cable, usually works. This is indeed the realm of signal distribution design, but it might just work by slapping it together. Give it a try. Come back here and tell us if some channels are iffy, if it worked great, if it totally sucked, whatever.