Yes, in theory an improvement of 1 dB should result in a change of as much as 10% better range, at least for unobstructed line-of-sight links. But such a change is very hard to notice in practical situations because multipath propagation (reflections) creates a very complex pattern of high and low signal levels at the receiving location, and the variation due to reflections can be higher than +/- 10 dB, so a 1 dB improvement may be swamped by this additional variation that is entirely dependent on location and the movement of objects near the radios and in the path.
The throughput (or error rate) improvement that you might get with 1 dB more signal depends on the kind of signalling/modulation you are using. For example, in 802.11a systems, 1 dB can make a significant difference.