Capt Bloggs:---
Good question, not something we see much in our operation flying from ILS to ILS, however.
In the Sim we recently diverted to Osaka Itami RJOO which has no ILS available in the data base, you select RWY 32L and build the approach from MIDOH. Then you must manually insert the ILS on the Rad Nav page.
So I guess the answer is---if no ILS is selected into the flight plan from the data base then the ILS will not auto tune.