No. Second seats (whether for the person themselves, or for their viola, etc) do not earn miles in any programme. Any attempts to achieve this outcome would breach the terms of most programmes, and you run the risk of having your account audited and closed.

Even if it were somehow possible to keep both bookings alive until checkin/boarding, how would you explain presenting two separate boarding passes at the gate to be scanned? (No miles for a no-show). And even if, by some subterfuge, you managed to get both boarding passes scanned - what happens when the head count shows that there is one passenger too few on board, and the flight is delayed while they try to sort out the problem?

Additionally, airlines that offer the ability to purchase a second seat stipulate that this must be done in a particular way (usually, bought at the same time in the same transaction, and sometimes there are even requirements for what must be filled in the name fields for that second seat). The airline must know that you are buying 2 seats together, so that they can ensure the seats are beside each other. Randomly/haphazardly ending up with a second, unrelated booking for the same flight does not meet the requirements for purchasing a second seat for a person of size.

As advised above - ring the airline. Explain the mistake, and they are very likely to waive any penalties or even give you a full refund if you're lucky.