will I listen to just the amplifier section of the integrated amp?
depends on whether you use an auxiliary input or a main in which bypasses the volume pot (not a great deal of difference really).
you will simply be feeding the LFD with an additional gain stage. If the LFD gain structure is adequate you will gain nothing. I would imagine the LFD is competently engineered in that regard.
Unless you definitely know that you are failing to achieve full rated power out of your amplifier due to inadequate gain (highly unlikely) I wouldn‘t bother. You will probably just add another veil to the sound.