Is it safe to use weathering effects that require white spirit to blend them, on a dried surface of Army Painter Anti-Shine Matt Varnish, sprayed from the can?

As long as varnish is acrylic, it should be fine. I do not know that brand so can not tell. But Future (Klear), Tamiya, Vallejo, etc. stand well the white spirit.

If the spray can is acrylic or lacquer based, it should be fine.

I'm wondering which weathering product you plan to use. Usually washes are applied to gloss or satin surfaces. I've seen some methods that use matte surfaces for filters but generally matte varnishes give a very absorbent surface. When you apply a pin wash, it might stain the surface and be very difficult to clean up.

I apply my overall wash to matte to impart a grimy dirty look.

I looked on their website and was unable to find any info on the type of paint they use i.e. oil or water based. If it's oil based (like floquil or modelmaster) the white spirit will take it straight off however if it is acrylic then you should be ok. One word of warning, some plastics seem to be badly affected by white spirit, to the point where the plastic becomes brittle or crumbles. I have had this happen on Tamiya and Italeri kits so if you ARE going to use WS look for the low odor (also called sansodour) kind and don't let it sit on the model too long. I normally put the model in front of a fan to speed up the evaporation of the carrier. I would suggest painting a scrap piece of plastic with the varnish first and use that as a testbed.

I've sprayed a test piece with the varnish and will try weathering it.

The weathering will be painting streaks then belending them using white spirit.

Looks like its Acrylic..

http://www.thewarstore.com/product39108.html

In my case, it works. But I usually start my work at least two or three days after varnishing. Have a good time~~~~