Hi E. - lot's of great advice on this site as always!
Your marriage is most important, so the important questions really are: Is it unsafe for your child? Does it spill over to the rest of the house? If not, then it is something you might have to live with, and I agree - go buy those curtains! But if it is a safety issue, then you need to discuss that you are concerned that your daughter may get hurt and can not be allowed in there. It may or may not make him think differently if his work area was viewed as "unsafe" for your child. If it is spilling over to other rooms, you should discuss your concern and feelings if it is effecting your quality of life throughout the rest of the home. Clearly, it get's to him at some point - because he cleans it up occassionally! I imagine the catalyst is ultimately not being able to function, or most likely, needing to find something!
Almost all successful business people can become even MORE effecient and successful- when better organized. Who knows how MUCH of his time is spent looking for or replacing things, or duplicating his efforts when that time could be spent making more money or spending more time with his family.
Instead of looking to convince him, because it is embarrasing you.. look for any signs that HE gives that it is a problem for HIM... such as frustration over something he can't find, stress over a late or missed deadline/opportunity. Let him know that you hate to see him stressed or upset over it and you want to help him find a solution with this vs. offering to CLEAN or organize his office :)
I am a Professional Organizer too, and yes, an organizer CAN help him be more productive, less stressed and more successful, but he has to be the one to want it and be HONEST about it. If he expresses he would like a better system, or that he is indeed frustrated at times, but is just too busy - get him an organizer for Christmas or his Birthday! Here is my website for more information about Professional Organizers, and my Blog ... there are some helpful tips and articles there. www.organizedbysandy.com and www.simplyorganizedbysandy.blogspot.com - Best of Luck to you!