How exactly are you using the wimax modem?
Is it like a portable hotspot device? If so, it creates a wi-fi network, which you then connect to using wi-fi on your portable device.
In this fashion, the tablet doesn't know and doesn't care what that network is.
In other words, using your wimax modem with your Nexus 7 would be no different than connecting your Nexus 7 to any other wireless network.
Their is truth in the statement that wireless will cause your battery life to deplete faster. It won't "ruin" a battery, but it won't last as long on a single charge as it would if you used the tablet without any internet connectivity whatsoever.
If you want to do anything other than read, listen or watch content you've already downloaded, you will need internet.
Being that you need internet access, using your wireless at home, using free wireless at a restaurant or coffee shop, or using your portable hotspot - they will all produce the same results for your tablet.