If your study of organizational culture involves perceptions of self within the organization, and probes for construals of roles within the organization and looks at the relationships between those construing, then RGT is viable. I recommend some like Idiogrid and doing something based on the classic RepGrid but using questions that suit your context. Consider the following:
Qualitative Methods in Organizational Research and Practice
By Gillian Symon, Catherine Cassell, Rosie Dickson
There is a large literature on the use of RGT in business applications. Please feel free to respond with more information so that I can be more helpful.
Yes. I developed one as part of my D.Phil (P.hd.) at Oxford in the 90's. It's based on the process of acculturation. There are two ways of doing it. One is longitudinal and the other is cross sectional.
its a bit difficult to describe in detail here but if you contact me I will share the methodology with you.