For some definition of "work" something like this might give you satisfactory results. You'd likely get more reliable answers if you explain exactly what your intended usage pattern is.
In short - the software has not been designed to operate in production on a read-only file system and likely few people, if anyone, is going to be able to give any kind of assurance that the system won't crash if operated in such a manner.
You will need to ensure that you have at least one read/write file system setup as a tablespace in the cluster so that large queries can make use of temporary result areas.
David J.