No it's not. The government won't own any shares that benefit from an increase in share price, nor will they receive dividends. The government can only receive the government aid back. It works as a forgivable loan. Loan-holders almost always come before equity-holders, and they could require full payment before dividends to equity holders.

Ideally, as grandparent notes, yes. But no, there's an obvious way out: Instead of paying dividends, reinvest would-be outgoing cash back into the company. On the phone, claim to follow the Amazon playbook. In addition to not having to give up anything to the government, the company might find itself improving!