Oh yeah, a 1060 should be fine, though you'll need to drop the detail settings on your followers. The Ryzen 5 1600 looks like it compares pretty well for multiboxing vs the 6700K (which I use). The RAM upgrade is definitely in order as modern clients can suck up 1.8+GB pretty easily, meaning 10-12GB should be kept available. The classic client should be a bit easier on RAM and CPU than the BofA client but it's always good to leave yourself some headroom.

Your biggest tool to make that system work will be the slot-swap macro.