Yes, you can do this -- I've done it up to Gen2 speeds.
However, we used PCIe packet switch ICs from PLX on both sides of the PCIe link. This is because these parts let you tweak via registers the exact link training behavior, in addition to signal parameters like emphasis / de-emphasis, boosting signal strength, etc.
They might have an app note on this now, not sure. The Gen2 parts no longer require a NDA, so you could pull up the data book for the 8604 or similar.
You could potentially build a simple x1 add-in card with a PEX8604 on board, one lane connected to the motherboard slot, and two off to SFP lanes.
The other side / target device would want the same chip on the other end. You could flexibly connect various ports on the 8604 based on strap options you toggle with DIP switches.