They will if they walk past them when they are "wandering", which is what they do when there is not an immediate need for them to check on a habitat or power/water facility, all of which have maintenance schedules, and don't have an assigned research task.
You need to do 3 things to get them to repair the vandalized stuff, that I can think of:
1. You need to have enough mechanics that they aren't completely tied up with higher priority work.
2. Not assign some of your mechanics to research.
3. Have their work zones set up such that they spend a lot of time walking on visitor paths and NOT staff paths....because the vandalized objects are on those visitor pathways.
Even doing all of the above, anything that is vandalized in areas that aren't covered by the mechanic work zones won't get repaired by them....they only wander between things in their work zone assignment. I solve this by placing atms strategically to use specifically in my caretaker and mechanic work zones that ensures they cover all visitor walkways.