ReadyNas 31200 ethernet ports

Your RN312 should be giving you about 100 MB/s on large file transfers.  That is close to the limit of what gigabit ethernet can carry. 

I'd start by testing the speed.  If you run windows, then use NasTester (found here: http://www.808.dk/?code-csharp-nas-performance).  That's convenient, and the results can be compared with what other users see.  If you don't use windows, you can try timing a large transfer (both read and write) with a stopwatch.

Also, you won't see any speed increase with a single client - since your single client is limited by a single gigabit connection.  The most you can expect is a modest performance boost when two or more wired gigabit clients are accessing the NAS at the same time.  For most home users, it isn't worth the trouble.

To your main question - you can use both NIC ports, but you can't just connect them both to your router or switch. You will need to configure the aggregation bonding method in the admin UI.  There are two options that will work with most router/switches - ALB and TLB.  The other two choices (LACP and Round Robin) require support for LACP or static LAG in the router or switch.  A couple of high end routers support LACP.  "Smart" or managed switches will support static LAG and/or LACP - but not the normal unmanaged ones.

Even TLB and ALB can sometimes misbehave on some home networks.  So if you see odd behavior, you should disable them and disconnect the second ethernet cable.