Once I load a new image, I want to copy my current running config back. If I saved the running config to NVRAM, will it still be there after I install the new image? Or do I need to send it to a tftp?
It is always good to backup your config. You never know what would go wrong after an image upgrade :)
Check your config-register. If it is set to 0x2142, it will ignore the startup config. To answer your question, changing the image should not affect your startup config or your saved config.
Also try saving the running config to bootflash or flash drives that you might have in your switch/router.
Here is also a link on Software upgrade procedure if you are interested.
Some software upgrades might even ask you if you want to erase flash before copying, doing so might even erase your saved config on flash.
Please rate post, if this helps.