If all the devices use your router as their gateway then, yes. You can just get the router to print out its arp cache. Log into the command line interface, change to enable mode (# prompt if you're not already there) and type:
term len 0
show ip arp
The arp cache timeout is 4 hours (14400 seconds) by default, so anything that's been actively passing traffic directly via the router (vs. via some downstream router or IP address on, say, a core switch) should show up in that output. (The first command isn't strictly necessary but it will keep the output from pausing every 20 lines or so by setting the terminal (output) length to zero or essentially as long as the output needs.)
