It depends on what format of media you're using, which will dictate your bandwidth requirements. Some example raw-format 24-bit (3-byte) colour video frame rates are computed below:
720p @ 30 FPS: (1280 x 720)px x 30 FPS x 3 bytes/px / (1024^2) = 79 MB/s
720p @ 60 FPS: (1280 x 720)px x 60 FPS x 3 bytes/px / (1024^2) = 158 MB/s
1080p @ 30 FPS: (1920 x 1080)px x 30 FPS x 3 bytes/px / (1024^2) = 178 MB/s
1080p @ 60 FPS: (1920 x 1080)px x 60 FPS x 3 bytes/px / (1024^2) = 356 MB/s
Assuming you're working with a SATA-3 solid state drive capable of the above throughput, and you're working with media that fits the above characteristics (specifically 1080p RAW video at 60 FPS), then yes, I would recommend the additional solid-state drive if near real-time rendering is a concern (and possible, given your existing hardware).
However, if you're working with compressed video, and your intermediate targets happen to be compressed as well, you will likely not benefit from the increased bandwidth. Furthermore, some rendering processes have the ability to "render to RAM", pushing out frames to storage in a buffered manner (effectively mitigating any speed gains you might get from a SSD to begin with).
TL,DR: It all depends on what your current hardware is capable of (in terms of rendering speed and throughput), how fast you need to see the results, the capabilities of your particular software suite (especially the renderer/encoder), and most importantly, what video format you're working with.
And for those looking into the future, as we progress past "Full HD" (1080p) to "Ultra HD" resolutions, the above bandwidth requirements will be drastically increased (e.g. a 4K UHDTV [double the resolution of 1080p] video will require over 711 MB/s bandwidth, uncompressed at 30 FPS and 24bpp colour). In these cases, until storage media can meet these bandwidth requirements, you may want to consider adding additional RAM to your computer, and performing the video processing on one or two dedicated RAM drives, which can provide performance on the order of gigabytes per second.