I am going to build a smaller wind shelter approximately 6x3 meters and using http://www.byggbeskrivningar.se/dimensionering to dimension the construction.

But I am wondering if and how it affects the span if you make Y against the support beam as in the picture?

A wooden shelter structure with a flat roof and diagonal braces, used as an example for beam span consideration in a construction project.
 
Now, I'm not a structural engineer, but logically that would mean you get the span between the diagonal braces instead of between the posts.

But perhaps you should look at the side loading on the outer posts, so they don't break.
 
Given the attachment is strong enough, you get a shorter supporting beam, which increases load-bearing capacity.

But most importantly, you increase the stiffness of the column construction in the left/right direction. This is mainly if you have an open construction; the board wall in the far wall does the same thing.
 
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