If a solo club member doesn't get blue ribbons, can they still participate in DL?

If they do not earn any ribbons during the week, they will not receive the team's weekly prize. But at the end of a league, they just need to be on the team to receive all of the league prizes that come from whichever division the team reached. So if the team was able to reach Sherlock Division by week 7, everyone including nonparticipants will receive all the of the Sherlock prizes.

Oh sorry, I misread this question at first. A solo player on his/her own team, who earns no ribbons will not receive any weekly prize. Whether they receive the prize from the Rookie Division, since they will never promote, I am not sure.