tl;dr = Quantity matters a lot; speed matters almost not at all.
Blender does "care" about system RAM quite a lot. Until the point that you're actually rendering, the whole scene resides in system memory. The amount of system memory you have will limit what you can make. Also, although Cycles is 100x faster on GPU, it can run on CPU.
Everything you make resides in system memory. If you have an enormous model that you want to decimate, you'll have to load the whole thing at some point. If you do any video editing, the more RAM you have will mean that more of your video can be cached, which helps with playback. Simulations tend to require a lot of RAM; more RAM means more options available to you.
As I alluded to above, although Cycles runs much faster on GPU, it will run on CPU. I have encountered cases where the scene simply couldn't be simplified, and I HAD to render it, but it was too big for GPU vRAM. Switch Cycles to CPU rendering, and although it took FOREVER, it did work. The CPU could use system RAM, and even virtual RAM to render something that occupied 40GB of memory. I.e. having enough system RAM might mean the difference between being able to render very slowly versus not being able to render at all.
All software will benefit from faster RAM. This is a very "low level" attribute, which means that none of the software on your system needs to be aware of nor specially coded for faster RAM. It will just be faster.
It's worth at least saying out loud that 10yo DDR2 will make your system noticeably less performant than the latest DDR5. I'm assuming that we're talking about choosing from among current-generation specifications.
That having been said, the difference between "slow" DDR4 and "fast" DDR4 is something I've found to be negligible and unnoticeable except for the most time-sensitive operations. (I mention DDR4; higher specifications are still new enough to warrant a lot of scrutiny; you'll want to do your own research at that point). I would recommend looking up benchmarks for the RAM you're considering, and compare their results. Blender Cycles is a common enough benchmark that you may even be able to find examples comparing various RAM speeds in the exact implementation you care about. My investigation shows that it's really not enough of a difference to notice, except for highly demanding real-time applications (games).