Presuming that all that got cut off are PCIE signal lanes, then of course it'd still work in a 16x slot.
In fact, everyone running an SLi mainboard is doing exactly that, with their twin 8x slots - only that in this case, lanes 8-15 are unconnected on the mainboard end. Chipsets that don't offer more than four lanes on the secondary slot (Intel, VIA) can nonetheless use the mechanical 16x slot, wiring only lanes 0-3 and leaving 4-15 unconnected.
In any such case, PCIE link negotiation will figure out that not all possible link width is hooked up, and will automatically degrade to what's been found working. In fact, you could even wire just 1x to your graphics card slot and it'd still work without any software intervention.
Having lanes missing on the graphics card instead ends you up in the same situation. As demonstrated by that PCIE 1x graphics card from Matrox, btw.