Does SSD reduce render time significantly?
It depends entirely on the type of rendering you are doing and the specs of your computer.  Bottle necks can occur in many different parts of the rendering pipeline.  Generally speaking, rendering is very GPU or CPU intensive, depending on if the render engine is CUDA (or similar) enabled.  If the renderer is able to utilize a GPU, then GPUs and/or dedicated encoding cards will generally provide the largest boost to performance if they have not already been optimized, if not GPU enabled, then CPU becomes the biggest factor if not extremely fast or doing very light rendering.

Memory is a potentially large factor as well and would compound with the hard drive.  If there is not enough storage space for the CPU or GPU to work on the video stream, then it will have to spend much more time moving data on and off the hard drive.  In this case (if the memory is showing high utilization during render) then increasing the amount of memory is likely to yield a significant improvement in performance.

Data transfer rate is still potentially a bottleneck though.  If rendering is very minimally CPU/GPU intensive and/or the system already have very high performing CPUs or GPUs, then it is possible that a HDD would not be able to keep the render engine supplied with data to process.

An easy way to tell if your disk drive is a problem is to look at how long the render takes relative to the rate at which you can playback video in the editor.  If you are encoding to a different drive than your source material is on, then if the HDD is a bottleneck, it would be expected that render speed should move at the same rate as you are able to playback.  If you can playback footage at 20fps, then your HDD is capable of feeding at least 20 frames per second (with no effects applied).  If the render engine is processing less than 20 frames a second, the processing speed is the limit.  If it is processing 20 frames a second, then it is entirely possible that the HDD is failing to keep the render engine supplied with data to process.

If you are storing the render on the same drive you are reading your source from, it becomes much harder to tell as a HDD requires moving the read/write head between where it is reading the source data and writing the render results.  This extra seek time will drastically slow the performance of the drive.  As a rule of thumb, I'd say to consider looking in to disk related solutions if your render time is better than 1/3 of the playback rate when reading and writing to the same drive, though I'd encourage trying to do a test on different drives for source and output to be more certain.  So, if you are reading and writing to the same drive and you can play back 30fps, then if your encoding is running at 10fps or higher, an SSD might be helpful. (As might more memory as that would reduce how often the system has to switch between reading and writing and help cover the gap.)