There is that double effect principle ...
No.
Firstly, because there is still the unresolved matter of whether taking the shot it formal or material cooperation (and if the former, then double effect does not apply).
Secondly, because the Vatican (upon whose rationale the SSPX appeals for the alleged moral liceity, if in fact it is material cooperation) laid out the criterion to be present for moral liceity vis-a-vis the covid vax, and they clearly have not been met. The SSPX cannot appeal to the Vatican to claim moral liceity, but then ignore its conditions, and substitute its own more convenient conditions.