Yes you can.
I'm not sure is it possible with APC ups-management software but you can do it with open-source NUT - "network ups tools". NUT consist of (1) handful of ups drivers, (2) ups daemon which communicates with the ups(es) through appropriate driver(s) and shares the information on the network (with some limited security controls), (3) ups monitor, which is monitoring messages from either local or remote ups daemon and performs required actions (shutdowns, messaging, mailing, whatever), and (4) some useful tools for changing ups configuration, sending commands to ups, logging.
So, on the "server side" you have an ups / upses with serial or usb connection to the host, ups driver(s) and ups daemon; on "client side" (local client also) you have unconnected ups and ups monitor. Sure, a "client configuration" is only feasible when the "client" host(s) is(are) connected to an ups monitored by the respective "server" host.
Inconvenience of NUT is that "server side" is operational on linux hosts only (or hosts with other unix-like OSes) while "client side" is operational also on windows hosts... so you need at least one linux per ups/ups group to benefit from NUT.
Otherwise, it works OK - very flexible and robust system, at least on APC hardware. I encountered just two problems, one is driver-, other - hardware-dependent. They are (1) usb-connection driver (usbhid-ups) is not specific for APC - and doesn't write lot of ups configuration parameters / log all info - so on newer hardware without serial ports better install a serial board or configure ups on an older machine; (2) in rare occasion (in fact, not so rare) when line power is restored after NUT sends shutdown signal to the ups AND before the ups shuts down (the grace period for the root file system unmount and final shutdown of the "server" host), the ups (or at least APC SmartUPSes) doesn't finish it's own shutdown and consequently, doesn't bring the connected hosts online :o(( Usually the shutdown signal goes to ups after the non-root file systems are already unmounted and the root file system have been remounted ro so there are no risks for your data and you can minimize the risk of unplanned downtime by setting the waiting period (ups.delay.shutdown variable) on the ups to 0, but APC should take care of this bug.