Reading this thread, the Home and Business version does support e-filing:
There are questions in this thread about two different products. TurboTax Business (for multi-member LLCs) and TurboTax Home & Business for individual filers.
TurboTax Home & Business will e-file CA Form 568 only for single member LLCs.
https://ttlc.intuit.com/community/business-taxes/discussion/does-turbo-tax-business-efile-ca-form-56...
