A mono jack is only capable of transmitting one channel. Technically, you can use stereo jack plugs on mono jack sockets and vice versa. But as soon as your chain contains just one mono element, the whole chain is reduced to mono. This means that you won't have the original stereo split in the result any more.
The reason is: for having a stereo signal, you will need an end-to-end chain of (minimum) 3 electric conductors. Mono jacks (or cables) only have 2 electric conductors.
You can send your stereo signal to a mono guitar pedal using a stereo jack plug. Depending on how the jack socket of the pedal is built, it will take up both channels of the stereo signal, or just one. If you want to know about it for that specific pedal, just try and check it out.
Using a second pedal on the second channel might lead to satisfying results, although the sound result can differ from a stereo-designed device because you are creating a dual-mono setup having no interaction between the two channels. It just depends on your intention. Generally speaking, if you are going for natural sounding rooms with reverb or delay effects, dual mono is not your best friend. Better go for a stereo effect pedal then.