Will ms lesions in brain show up as well on mri when not having "flare up"?

They can: Between MS flares, new brain lesions may develop. However, depending on various factors including location, they may not cause symptoms. These are called subclinical lesions. Refs: http://www.medscape.com/viewarticle/811594_print , http://www.jwatch.org/na32467/2013/10/04/mri-subclinical-ms-disease-activity-surrogate-clinical , http://www.nap.edu/catalog.php?record_id=10031

YES: If you possess MS, and not having a relapse, some T-2 lesions can be invariably present, but the location and size may fluctuate. During a relapse, often can see Gadolinium positive T-1 lesions, which can be discovered over a period of about 4-5 weeks.