An MRI is a pretty big gun for a backache after strenuous activity, especially if you do not have any "red flags" for a significant back injury. And it is expensive.
But, yes, an MRI will reveal edema (blood) in the muscle, if it has been torn. If it is just due to muscle soreness from lactic acid build up, like the soreness you see when starting a new activity, the MRI will not pick that up.
The MRI is based on hydrogen atoms, and the more hydrogen atoms in a tissue, the better it will delineate the anatomy. So, tissues that have a lot of water in them (H2O), will show up as white on MRI; things like fat, fluid, blood, etc. Muscle is intermediate, so it appears in shades of grey. Cortical bone and tendons appear black, as they have little water in them.