That would be fantastic. Speculations and possibly too obvious stuff follows:
With the LPF unpopulated you could place the resonant LC under test between the C28 and C27 points and use the already present signal injection to sweep and detect the peak. BPF would need to be disabled, like disconnecting C1 or similar.
If you want to have the entire LPF fitted it would be possible to redirect R34 to get the signal off board via the LC under test and fed into the BNC, or perhaps after C29.
The rest is firmware (: Auto/manual sweeping for finding the peak and perhaps tuning the coils etc.