No, I think just because the range is in within (-1, 1) does not make Tanh a good choice. The reason is the distribution of your output will be shifted more towards the two ends  -1 and +1, so most of your outputs will be close to -1 and +1, while very few values will be close to 0. So, assuming that your target values are uniformly distributed within [-1, 1], Tanh will not be able to generate outputs that match the target distribution.