Yeah you could, if you use the telnet interface.
telnet localhost 11666
user Username
pass Password
status
You will get a reply like:
251 Urdd server status.
Uptime: 3 days 20:23:32
Queued: 0
Running: 0
Scheduled: 1
Users: 1
If Running is 0, nothing is going on at the moment.
However, scheduled tasks (such as updating newsgroups) won't work when the server is powered down