I think OP intended to ask if they could just give their UA Gold physical card to their co-passenger to avoid checked bag fee. That would be a clear violation of airlines FF policy. If the agent compared names on physical card and boarding pass, they could flag both the accounts for internal follow-up (rare).

Bag fees are a very profitable endeavor for the airlines. Get a CC with baggage benefits if you expect to fly that airline more than 2-3 times a year. With United Chase Explorer Card, ($99 annual fee), you get free bag, primary car rental, 2 club passes, 25% WiFi discount among other benefits. It’s a no-brainer for entry level flyers.