From SWTOR’s Forum’s Suggestion Box, somebody asked if you can get your Companion character to fly back to town, “Sell all grays” (loot that is useful only as vendor trash to generate cash). GeorgZoeller, a Bio Rep, writes:
In TOR, you indeed have the option to command your faithful (or scornful) companion to make a trip to the nearest market to lighten your backpack and fatten your wallet by selling objects of purely monetary value.
As you command your (possibly hateful or even loving) companion to do so, which they will only agree to if you are not engaged in hostile activities and they are convinced your life is not in immediate danger, they will arrange for quick transport to the closest market and return after a short while (roughly a minute, subject to tuning) with your hard earned money.
It is assumed you trust your (trustworthy) companion in so far as to accept whatever they tell you in regards to the prices they negotiated and will not undermine your (purely professional) working relationship with them with potentially insulting questions about taxes, fees, union dues and other applicable fees.
In other words, yes you can do that.