The RAM will not work, because the 560 only supports the ram is max 2GB 1333MHz (PC3-10600) per slot and total 4GB (2 X2GB).
From Dell: ftp://ftp.dell.com/Manuals/all-products/esuprt_desktop/esuprt_inspiron_desktop/inspiron-560_User%27s%20Guide_en-us.pdf
Actually it is 8GB supported total from this guide, yes 1600 will be downclocked to 1333, tested on Inspiron 570, which is sibling of 560.
I think that maximum amount of memory can go up to 16GB, since it is possible for Inspiron 570, I am using 2x4GB configuration. Avoid fancy timing memory, Crucial and Corsair are most likely ones which will work well, others could have problems.