From the way FCL.915.FI is worded, it does appear so, but it is not crystal clear. It says that when you apply for an FI(A) as a PPL(A), you should meet "the requirements for CPL theoretical knowledge, except for an FI(A) providing training for the LAPL(A) only".
When the FI(A) rating is added to the licence there should in theory be an entry in the remarks column stating that the rating is restricted to giving instruction for the LAPL. Whether or not that is there in practice is another matter. There is no reason why a FI(A) with no CPL theory should not teach for class or type ratings as they have met all the requirements for the issue of a CRI rating! Perhaps you should obtain that at the same time!