Should someone borrow from a Gemach if he has invested (not on-hand) savings he doesn’t wish to touch, (but theoretically could pull some money out), and he needs money to get through a tough time? Or should the Gemach money be only for people who have very little savings at all?

Most Gemach's have policies which determine valid approved uses. Many Gemachim are available for loans in the situation you described, and taking such a loan wil not deprive others of taking a loan as well. Many other Gemachim limit loans to people in particularly dire circumstances, or for specific needs (e.g. weddings, medical expenses, getting out of debt). There is no halachic demand to become destitute before availing oneself of a Gemach. Gemachim are often available for people to use for investment (starting a business, not buying stocks). Ask the administartor of the Gemach what the policy is.