I would do a search on discussions "roman shade linen". There are a number of fabric/curtain specialist Houzzers on here who will also step on on this question.

Not only does linen wrinkle, but it stretches and shrinks too. :(
If you are thinking about a traditional flat roman shade--it opens and shuts creating folds in the fabric. Imagine what a linen that wrinkles will look like in those folds when the shade is down. There are different styles of roman shades--that could be better suited to linen, but I would not recommend a flat roman shade. Have you considered a linen look--incorporating a man made fiber? Would have more stability.

There are good linens and then there are cheap linens.......all look OK when the shade is pulled up. When the shade is down they all look bad. Come to think of it..most roman shades when they are down do not look great in my opinion as the folds are still evident in all fabrics.

The wrinkling and the sagging is a design element often in casual slouchy, beachy type interiors, and it is a look that you either love or hate. If you want crisp and neat, most linens won't produce that look, some will though.

Do you have a specific linen in mind?

Actually here is a shade in my son's room made of 100% linen from ROMO fabrics...this linen is crisp, not saggy and does look good when let down. These have been hanging for at least 3 years and have always looked good. Maybe a little beat up from his use.
This linen was not cheap..in the $100 per yd region, but a very good quality Italian linen. No sagging.

thank you everyone!