Theoretically, if the washers you use are conductive there shouldn't be a problem with grounding the board, but raising it will mean it'll be out of alignment with the back plate. If you need only a little clearance you could raise just the end of the board opposite the backplate but be aware that the board will flex.
If the washers are too wide you also risk shorting the board, so keep them small.
Also, you need to consider your heat-sink and weather it'll fit. If it's a very tall performance heat-sink in a small case you might not have room to replace the side of the PC if the board is raised (it's happened to me with a Cogage Arrow and a mini-atx), especially if you have a fan mounted on the inside of the side of the case to cool the IO cards, but one way around that is to mount the fan on the outside of the case (which I do a lot but which might not be agreeable to you)).
Edit: Just saw that the alignment with the back plate is the problem. Should have read the post a bit closer ;0)