First up, I love the wall bed. Looks like a solid purchase. And it’s so neat when closed up.
Now, on to your question.
Looking at the SVALNÄS desk, IMHO, it’ll take more effort than what it’s worth to make it work. The SVALNÄS side posts will not be wide enough to accommodate the IVAR hinge and to hold the SVALNÄS desk flush between the posts in upright position. (You’ll need to make a new thicker frame like in the IVAR.)
And because of the extra margin needed for the hinge, the back of the desk will not be flush against the wall, as in the original design. You’ll need to figure out how to keep the desk in horizontal position with an extra horizontal brace and hinges. All these will add up to your cost. If you’re trying to save, it may not be the best way to go. But can it work, maybe? It won’t be easy.
Alternative wall mounted tables
I would rather go for a simpler drop leaf desk like the NORBO or NORBERG. It does not have drawers like the SVALNÄS desk but with the up and down movement, I can’t imagine drawers being very useful.
NORBERG drop leaf table | NORBO drop leaf table | IKEA.com
With the drop leaf table, I’ll just need to figure out how to keep it closed when not in use and bed is in down position. Perhaps a magnetic latch will work. Or less visually appealing, string, like how the wall bed mattress is kept in position when upright.
How about foldable table brackets?
I would look outside of the IKEA range for a neater foldable table solution. How about using these folding table brackets and cutting a piece of wood to match the entire width of the bed for a nice fitting desk? Or get a ready made one like this: