Most machines can be used for soft furnishings, that one is probably fine but most would struggle with the sort of layers you describe.
But, you don't really want to be sewing through the blind tbh, there is a big chance that it won't hang properly.
I have always made my own blinds and apart from attaching the velcro and sewing the rod pockets or sewing the tape on, which ever method you are using, I don't use my machine.
I do it like this - mark and sew rod pockets on lining. Lay fabric on table, bump on top, lining on top, turn under and pin side and bottom edges and before you take it off the table put a few pins across the blind between each rod pocket.
Hand sew hems at edge and sides. Back on table. Put velcro on the fabric at the top and sew it on. Turn top edge over so that velcro is now on the lining side, pin and hand stitch.
Hang it and sew invisible single stab stitches through everything a few times here and there, usually just under a rod pocket.
If you sew through the whole thing and it is slightly off anywhere it won't hang properly, invisible hand sewing looks nicer.
I think that an unlined blind in a heavy linen could possibly look ok with machine sewing but I have never done it.