In that case Drinkhall, Andrew Baggaley, Liam Pitchford, Joanna Parker, Kelly Sibley and Na Liu would need to reach the later stages of the competition in Luxembourg.
Failing that, the squad have one more chance to qualify by right in a final World Olympic Qualification Tournament in Qatar from 10-13 May.
Britain's top woman Parker, currently 136th in the world rankings, told BBC Sport: "I'm in a good position [to be selected for the Games] at the moment but there's still time to go. It's not all about being selected, it's also about competing once you get there."
GB Table Tennis are expected to announce their final Olympic squad on 31 May.
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