Mechanical versus electrical PCI-Express on PowerEdge R515

Yes, it works just fine, obviously it's only work at x4 speed (8Gbps).

I would check whether the x16 slot can handle the power load of the x4 adapter, it depends on the adapter but I've seen some quite high power draw adapters using x4 electricals without an external power connector such as those you see in higher-end video cards. In some cases system-board manufacturers expect that adapters going into x16 slots will usually use external power connectors so they rate them with a slightly lower power draw capability from the board than from the lower-speed slots. This probably won't matter in your case but I wanted you to be aware.

Any PCI Express card of a smaller size will fit into a larger slot. So an x1 card will fit in an x8 slot. Please see the Wikipedia article for more info on the spec.