The best you could do, is replace your motherboard for one that suits the purpose you are intending. Barring that, if you were brave and like to tinker would be to open the ends of the x1 slot you wished to use so that you can physically insert the longer card into it. Electrically, all PCI-e cards are compatible, and the only thing that will be missing are the extra PCI-e lanes. All that is needed is to remove the plastic that is preventing the insertion of the x16 card. Do not remove the plastic "key" that is in the slot, just the socket's end plastic, preventing the insertion. Understand of course that this still does not guarantee you will be able to insert the card, as there could be other components in line with the slot that could physically block a long graphics card.
There is no electrical benefit to the adapter, as it can't increase the number of PCI-e lanes the card will receive, but only give the card a physically compatible socket.
Another problem you will face if you choose to use an adapter, is the card's inability to line up with the chassis mounts once you have adapted it, making it more difficult to secure. Along with this problem, you may find the card is no longer close enough for a CrossFire bridge to reach it without putting stress on the card or the bridge, and you will not be able to enable CrossFire without a bridge.
If you attempt to open the ends of the motherboard's slot, understand the risk of damage to the slot, motherboard, and any graphics card you insert into it, if performed incorrectly, is something you're going to have to accept for yourself.
Tip to using a Dremel tool to cut open a PCI-e x1 slot:
http://blog.zorinaq.com/?e=53
If you look closely at the end of the PCI-e x4 slot closest to the "USB 3.0" label, you will see that it has been left open by the manufacturer to accommodate longer cards being inserted. This really is the only modification needed on x1 slots to allow for longer cards:
http://images.bit-tech.net/content_images/2011/11/back-in-black/sapphirea75mboard7-1280x1024.jpg
As my previous link recommends however, if you use something such as a spinning disc cutter to open the end, do not run the disc parallel to the slot, but perpendicular, to avoid cutting the conductors in the slot in the process.
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