Don't think so, a video of this size can be written in 1-2s by a modern HDD. So give it some additional seconds for seeks, and you're still on the safe side.
This is just a test video - I assume the videos Dave would actually be encoding would be much much larger - which is what I was referring to.
This has nothing to do with the final file size, it is to do with the write data rate. A modern decent mechanical HDD is able to write at around 110MB/s, and the transfer to the disk is handled by DMA, so it is completely offloaded from the CPU, using a SSD, or even a RAID0 SSD array would only help on the load/read stage during video editing, not encoding. What would be more beneficial here would be loads of RAM, talking 8GB+.
Also, setting up a RAID0 anything array is just asking for trouble, loose one disk and you loose everything, if you want to go down this path get an additional disk and setup RAID5 (Stripe with parity), or for better performance with redundancy go for RAID10 (that is RAID1 + RAID0, so clone & stripe). If you are using SSDs in a RAID array and really do need that kind of performance, get a real RAID card, do not use your so called 'RAID' function of your motherboard, as it is software RAID and is all done on the CPU.
Honestly though, those that need striped SSDs are just kidding themselves, I work in the hosting industry and we only every deploy these configurations to servers where they have 100GB+ databases and enormous I/O on them, which you never see in your day to day usage on your desktop computer, and even then we usually opt for more RAM first (32GB or more) so we can cache everything we can as RAM is loads faster.
Here is a cost estimation for a RAID6 array:
120GB SSD = ~$300
6Gb/s RAID Controller = ~$200
Total = ~$500
And cost estimation for a stack of RAM which is hundreds of times faster then any SSD:
32GB DDR3 RAM = ~$250-$300
But... Don't get me wrong here, I love SSDs and I use them in my Desktop and Laptop and would never go back to a mechanical HDD for my OS disk, and I would love a RAID10 SSD array, but the amount of times that I would actually use it to its full potential would be very very rare, and shaving 500ms off a disk wide search for a file just is not worth the cost.
Also, I often grep enormous directories with tens of thousands of files that contain projects such as XBMC or Openbricks which contains the linux kernel source + every source file you could need for a basic GNU system and find it only takes a few seconds on a single standard SSD, I do not see RAID giving me enough of a performance boost here to warrant the cost.