I would to know if end devices uses a router to reach a coordinator in transparent mode.

all these point to the coordinator and coordinator is in broadcast.

end_dev <–> router <–> coordinator

which product are you referring to? Keep in mind that there are more than one type of XBee product all based off of different protocols and frequencies. But if it is the Zigbee versions, then you can use Source Routing to see the path and control the path a data packet takes.