Hi there,
To answer your question, yes you could use the Probe software on a Raspberry Pi to discover the router. Indeed, you would most likely not need to have the Probe on the same VLAN as the router, because in most cases, the probe will successfully discover and connect to devices across VLANs, and certainly it should based on the description of your network.
The downside of this approach is that, while the FindIT Utility running on Windows is a simple discovery tool and is very straightforward, the FindIT Probe for part of a more full featured network management system, and should be use in conjunction with the FindIT Network Manager software. Depending on exactly what you are trying to do, you may find all that functionality very useful and worth the additional effort of setting it up, or it might be like using a sledge hammer to swat a mosquito. Certainly the FindIT Probe/Manager combination will do basically everything the Utility does, plus a lot more. But using the Probe+Manager is a bit more involved than using the Utility.
Hope that helps a little bit.
Cheers,
Dave.