Edit: I was wrong.
Short answer: Most likely yes, as long as the vaxxed are creating the spike protein.
A study from St. Joseph Hospital Phoenix AZ demonstrates the production of exosomes with spikes on them that circulate in the blood after mRNA vaccines. The immune system learns to fight against the exosomes with SARS-CoV-2 spike protein too (they are "immunogenic"). If you transfer them to another organism, they are immunogenic there too (as shown in mice): https://www.jimmunol.org/content/207/10/2405
Dr. Mobeen Syed on this study: https://odysee.com/@DrMobeenSyed:1/summary-vaccine-generated-spike-proteins:e
Thank you, very interesting paper; I've removed my previous answer in the face of new and better information.
(post is archived)