The SSD won't help with render times, but it will help with file read/write times. So if you're dealing with high bitrates (reading from raw video, writing to very lightly compressed video or slightly compressed 4k video), the SSD will help.
Likewise, if you're pulling from lots of different video files to combine them into a single new video (real video editing like a movie or TV show, not simply re-rendering captured raw gameplay footage), the SSD's faster ability to switch between reading different source video files will help. (I'm assuming the source video files are too big to pre-load into RAM.)
The biggest speed boost is if you're doing this in real-time (real-time video editing). Then the SSD helps tremendously to reduce or eliminate the lag while you wait for the video source files to be read. I'd almost consider it a requirement in this case.
It's also worth mentioning that HDDs suck at simultaneously handling two (or more) read/write requests, while SSDs don't even blink at it. So even though the CPU is barely working, if the video editing/rendering is doing a lot of disk activity, the computer will be useless for other tasks. That's why an anti-virus scan on a HDD computer brings your productivity to a grinding halt. With a SSD, you can run a render in the background and pretty much continue to use the computer as if it weren't rendering at all. With some judicious assignment of threads to cores and thread prioritization, you can even play games on the computer while it's rendering. The game runs at close to full speed while the render only uses spare CPU cycles. It's not ideal, but it beats watching TV or buying a second computer.