I would not be comfortable with the club simply hoping a medical emergency does not happen on the weeks the trained people are away.
The exact requirement can depend on the club, competition and role, so I would get the club secretary or welfare lead to confirm what cover is required rather than guessing.
Operationally, though, you want somebody present who is appropriately trained for the first-aid response the session may require.
England Football’s Introduction to First Aid in Football course is designed for people working with players and the certificate is valid for three years, so having a wider pool of trained coaches or volunteers is sensible.
I would also keep expiry dates visible centrally rather than discover a gap on the day.
First aid is not a specialist job you improvise between drills.
The club should know who is trained, who is present and what the emergency plan is before the session starts.