At the risk of sounding like a smartass - depends on the linen. Linen comes in many different weights/weaves. Linen will wrinkle at lighter weights and rumple at heavier weights - it's an (IMO) casual cloth so its suitability may vary for you.
If you want something that is 'versatile' yet not as ubiquitous as the dark navy blazer the solution is simple - get a light navy one. There are many shades out there - some here like 'air force' blue, others 'light navy', and yet others other shades.
IMO a good weave for 'multiple season' wear would be something lighter, breathable (i.e. porous weave) and wool-based, maybe with a touch of mohair. You will have to compromise and decide whether you want this to be a spring-summer-autumn jacket or a autumn-winter-spring jacket because no fabric is going to be comfortable to wear in all 4 seasons. Don't get a flat finish worsted fabric or you will look to the SF folk like you are wearing an orphaned suit jacket.
Talk to your tailor if you are getting this made up.