The answer is maybe. Executive Club Silver and Gold card holders are generally granted access to BA lounges when travelling on BA coded flights operated by non-oneworld carriers. At BCN where there is no BA lounge, access to the Sala Miró is provided under an arrangement between the lounge operator and BA. There may be local conditions in place that would allow a BA Silver to use the lounge when travelling on BA code/VY metal.
You can contact the lounge directly by email:
[email protected]
Failing that, paid access is an option at €25.50 per person