Not the whole team is involved in this type of testing to avoid the wastage of time of all the QA’s.
Smoke Testing is ideally performed by the QA lead who decides based on the result as for whether to pass the build to the team for further testing or reject it. Or in the absence of the lead, the QA’s themselves can also perform this testing.
At times, when the project is a large scale one, a group of QA can also perform this testing to check for any showstoppers. But this is not so in the case of SCRUM because SCRUM is a flat structure with no Leads or Managers and each tester has their own responsibilities towards their stories.
Hence individual QA’s perform this testing for the stories that they own.