We don't know the answer to this. It may work or it may not. I would see if you could borrow one to try before committing to purchase.
Hope this helps,
Although I don't have a GTX1060 I was able to test my I7-3820 setup with a GTX 980 4GB (Also a PCI Express 3.0 card) and works fine in a PCI Express 2.0 slot in combination with the i7-3820.
normally this card runs in an older system with a PCI Express 1.0 slot in a Pentium D965 EE system.