It depends on what you are doing with it.
A newer Atom will handle it just fine, though if you are using 10GbE and RAID in the thing, no, it won't keep up.
SMB multichannel even, and it should be fine for a couple of gigabits of bandwidth, basic RAID rebuilds, etc.
I'd personally look at an inexpensive H97 board and a Haswell Celeron or Pentium processor.
Odds are excellent you'd cut idle power consumption to a quarter of what that AM2 system will use.
I had an AM2 based SEMPRON (I think it was AM2), which is lower power consumption than what you are looking at. With a single 2TB drive and all board features disabled that I wasn't using, a single 2GB DDR3, and a bronze rated PSU...it was using about 38w at idle with the drive spun down.
My current Ivy Bridge based Celeron with an mini atx H77 board, 8GB of RAM, an SSD boot drive, a pair of 2TB drives in RAID0 and a pair of NICs (before I was using the on board, now I am using a pair of Intel single port NICs) with the exact same PSU, it uses 21w at idle.
That is $17 a year in operation efficiency difference, with more RAM, an extra drive and extra NICs. That old system if it was spec'd similar likely would have been more like 42-45w idle...
Considering how cheap it is to get a "low end" board and a low end processor and as much more power efficient it would be, just do it. For a probably $1000+ build (all those drives) an extra $100 in costs for what might well be $20-30 a year in electrical savings (could be more, especially in anything other than idle, actual operation is likely to be a bigger power delta), you might as well.
Also look for a nice robust PSU.
Also consider fewer higher capacity drives and reasonable spin down timers (15 drives at idle is probably going to burn 80-100w of power, spun down, likely 5-15w of power).
Unless you are looking at 15 salvaged drives of low capacity, that is a MASSIVE amount of storage (even if some of it is duplicate volumes).
My suggestion is, if some of it is RAID5/6, don't. Just have a backup volume to backup the primary volume to. Better redundancy, and if it is a RAID5/6 backup of a RAID5/6 volume, you just saved several drives.
Also, the more drives, the greater the likelihood that one is going to fail. If the volume is already backed-up, preferably with two back-ups, your butt is already covered if one big drive fails.
Three 4TB drives for a primary and three 4TB drives for the back-up volume is going to use a LOT less power and also allow you to have a much smaller PSU than six 2TB drives for primary and six 2TB drives for back-up.
It'll also be quieter, produce less heat and likely cost less to (as 3 and 4TB drives currently seem to be the $ for capacity sweet spot).