Normally no if your “improve” means to get a better video.
The source video from the HDMI cable is newly digital signal, like DVD, Blu-Ray and cable TV, which is almost without loss of quality, but your old TV is an analog TV. When you convert your digital video to analog AV signal , the converter will decoded the digital signal first, upsampling it , and then build it to analog signal, in this procedure the converter will never get the video to be better than the original. And the RCA cable is less immune to noise and the video will reach the display with inherent less quality also.
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