That is exactly how they did it. Thus the AGM-88E. That is one bad ass HARM. Turn your radar off or go passive....it wont care, it already has pinpointed your location via INS/GPS. Here is some good info on it I found.
System
• The AGM-88E AARGM is the follow-on to the
AGM‑88B/C/D High Speed Anti-Radiation Missile (HARM)
using a modified HARM body and fins. AARGM is employed
on F/A-18C/D/E/F/G platforms.
• The AARGM incorporates Millimeter Wave (MMW), GPS,
and digital Anti-Radiation Homing (ARH) guidance, a
Weapon Impact Assessment transmitter, and an Integrated
Broadcast Service Receiver (IBS-R).
- MMW technology allows enhanced target discrimination
during terminal weapon guidance
ARH improvements over HARM include an increased
field-of-view and larger frequency range
- The GPS allows position accuracy in location, time, and
weapon impact assessment transmissions
- The IBS-R enables reception of national broadcast data