No, this will not and cannot work unless the receiving device uses asynchonous sampling rate converters on its inputs. I've never seen a piece of consumer gear with this capability.
The four devices producing the S/P-DIF signals can't be assumed to be synched to the same master clock. As a result, the 8-channel receiving interface would get four different clocks, each of which is at a slightly different frequency and in random phase relationship to all the others. There's no way to synch and interleave those signals into an ADAT data stream, unless (as I said) they can be converted to a common clock--and that would be a rather expensive bit of signal processing if it's to be done well by modern standards.
So basically, no. You might find the inverse--an ADAT-driven device that produces four S/P-DIF output streams, but probably not the configuration you're looking for.
--best regards