As much as programmers hate to document their code/system and draw UML (especially, Sequencing, Activity and State machine diagrams) or other diagramming notation, would you agree to do it if it kept managers from requesting a "minor change" every couple of weeks?

IOW, would you put together visual models to document the system if it helped you demonstrate to managers what the effect of changes are and why it takes so long to implement them?

(Edited to help programmers understand what type of answer I'm looking for.)

2nd edit: Restating my question again, "Would you be willing to use some diagramming notation, against your better nature as a programmer, if it helped you manage change requests?"

This question isn't asking if there might be something wrong with the process. It's a given that there's something wrong with the process. Would you be willing to do more work to improve it?