I wouldn't know how to distinguish all of these calls for protest lately from astroturfing campaigns.
Are there really no institutions left in the US you can rally behind and who are big and experienced enough to call for organised protests? What are the biggest non-governmental progressive or liberal institutions in the US anyway?
Unlikely, they're happy with their result.
It's however possible that the conservatives will run the Austrian playbook. Talks with the social democrats fail, "we have a responsibility to Germany to form a government", then make a coalition with the AfD (Nazis).
Back to your original question: the BSW will likely contest the elections, as they have missed the 5% threshold by only ~14k votes and there are evident irregularities. For example, many Germans living abroad, for example those living in the US, had almost no chance to cast their vote.