No need to assume. Just check your policy document and find out the exclusions lah.

This is one of the exclusions from my policy- Sickness or Injury arising from illegal activities, playing professional sports, racing of any kind (except foot racing) or hazardous sports such as but not limited to skydiving, base jumping, cliff diving, flying in an unlicensed aircraft or as a learner, martial arts, free climbing, mountaineering with or without ropes, water skiing, scuba diving to a depth of more than 10 metres, trekking to a height of over 2,500 metres, bungee jumping, canyoning, hang gliding, paragliding or micro lighting, parachuting, potholing, skiing off piste or any other winter sports activity carried out off piste.

Judging from the "hazardous sports" listed, I'm sure badminton as a hobby is not a problem. Only if I'm a professional badminton player will it be excluded I think.

If not sure just email your agent or insurance company.
As long as you disclose everything, it shouldn't be a problem.