NO!
On the Shimano M324 in your example the toeclip/cage side , steel is on the opposite side of the pedal
so you drag the toe clip, down facing , when using the SPuD cleat..
maybe the Spin Class machines BB are high enough off the ground to have this not matter..

there were accessory toeclip/strap/cleats, made to use regular shoes on Look Type pedals .
IDK if there are SPD versions ..


For high powered track racing , straps are added to racing pedals and shoes

to reinforce the cleat shoe interface, so you,

the Sir Chris Hoy types, don't pull the glued upper out of the sole of the shoe..