I have a 2008 Chevy Tahoe Hybrid. I was thinking about installing a after market remote start. I was wondering if installing the remote start would cause and issue with the battery. I like the idea of a after market remote start due to the fact of better range.

I think the 12V system as far as I have experimented with is a very straight forward system just like any other car. You want to make sure that the installer is good or get a guarantee from them that no systems would be compromised.
Remember that the 12V BATTERY is fairly specific to the vehicle and you don't want to drain it prematurely or you will have all manner of start issues. I have had the dealer replace my battery twice, once due to the wrong battery being installed during build and once due to a dead cell. With this situation, if the radio was left on and the engine shut off, the car would not turn over until the battery recovered or was jumped.