In the case of the LAPL the flight would have to be conducted at a DTO or ATO and the aircratft would have to be notified as part of the Declaration or Approval. As its outside the weight range it would probably not be accepted.
In the case of the NPPL, there is nothing in the ANO to prohibit training in an aircraft that does not meet the definition of a SSEA but is in the same class. The cost might put a few off.