I understand that hybrids offer and advantage to the system overall (page file, boot time, etc). But does a hybrid drive provide an advantage in terms of writing large files? My first intuition says NO because the volatile region meant serve as a cache which makes for better reading. But and am still looking into how hybrids work and I could be wrong.
It depends on what you mean as hybrids.
Seagate has a line of drives which as essentially HDDs, but with 16GB or 32GB flash cache. The firmware on these drives keeps track of which blocks (not files, blocks) are read a lot and keep a copy of the most read blocks in the flash (SSD-like) part of the drive.
Writing to these drives will not be any faster.
Another way which was recently mentioned as 'hybrid' is in fact a plain old HDD and a separate SSD. Using the right chips and the right drivers you can do something similar to the Seagate hybrids. Precisely how this works is unclear to me. Nor does it seem to offer any significant advantages over just using a SSD for OS and most accessed files and a HDD for mass storage. (Though it requires a bit more thinking when you set it up).
In your scenario, a hybrid drive is no different than any other drive with a large cache. Once you fill the cache, you're limited to the write speed of the drive itself. But in most real situations, your writes aren't the only traffic contending for bandwidth. There are other reads and writes going on to serve other activities and some of that will be served from the cache rather than contending for bandwidth to the drive.