Yes, IKEA bulbs are generally good Zigbee repeaters in a smartthings setup, provided, of course, that the bulb has power, even if it looks like it’s off. See the community FAQ:
FAQ: Are Smart Bulbs Repeaters? (Updated 2019: the new answer is yes, but may be inconsistent)
A few individual community members have reported issues with them, so there may be a bit of trial and error to see how they work at your location.
As to seeing the routing, unfortunately, smartthings does not give us any tools to do that. 
Some community members have bought a third-party device, added it to their network, and then used its tools to get the route maps, but it can require some technical skills to get set up and of course it’s additional cost. 