Hey,
Yes, you can trigger an ADF/Synapse pipeline via Azure function by leveraging the REST API for the same.
Synapse: https://learn.microsoft.com/en-us/rest/api/synapse/data-plane/pipeline/create-pipeline-run?tabs=HTTP
ADF : https://learn.microsoft.com/en-us/rest/api/datafactory/pipelines/create-run?tabs=HTTP
You can use Managed identity by granting the Azure function necessary access on the ADF/Synapse