Depending on the resolution you are looking at this has the potential to work. When looking at the data you are trying to pass, you should always half the amount of potential data.
For a 1GB connection, you should expect to get around 512mb/sec. So if you are prores, you are about 140mb/sec. Avid, DNX 145mb/sec.
But remember, storage performance is about low latency, not just bandwidth. So the responsiveness of your array may be poor, even though you have plenty of bandwith to the box.
The Synology is typically intended as a network parking place. There are several Synology options that including iScsi. Which is essentially gigabit ethernet that is optimized for high bandwidth connections.
Typically you have a NAS, like a Synology connected with multiple Gig connections or a 10GB connection to a switch so you can get as much throughput to the storage as possible. If you had 2 Avids there would be a few tricks you would have to do to make it work.
You should be fine, but I would be concerned about the real-time functionality you would get.
I know it is more expensive, but you should consider some of the smalltree solutions. They are esentially computers with high bandwidth storage attached, and multiple network connections to a switch or to computers direct connected.
I work for a reseller that sells several high bandwidth options, but for 2 systems you may simply consider a smalltree rig.
Thanks
James