Yes, and Silvaire is, of course, correct. 61.51(a) requires each person to document and record "Training and aeronautical experience used to meet the requirements for a certificate, rating, or flight review of this part." and "The aeronautical experience required for meeting the recent flight experience requirements of this part." It does not require time that is not used for either of those purposes to be recorded at all.
61.51(b) then requires that if a flight is logged certain information must be recorded . However, it does not, as you seem to imply, require every flight or lesson to be logged