No.
The criteria for leaving trust are:
Positive - You trust this person or had a successful trade.
Neutral - Comments. Your rating will not affect this person's trust score.
Negative - You were scammed or you strongly believe that this person is a scammer.
For the visible green/red trust summary over there <------ , it must be left by someone who is on either the default trust list or you have added to your trust list for you to see it.
If I decided you were worth a trust rating and feedback for one of the above reasons, it wouldn't show in the summary to anyone who hadn't added me to their trusted list, but would be listed on your profile under "untrusted feedback".