Yes, you are absolutely right. Certain combat engineer units, such as my dad's were independent units. At several points in time the 540th were attached to the 3rd, 34th, 36th and 45th Infantry Divisions on an as needed basis. Other engineer units were a permanent part of a division, so of course following their journey across the European continent would be much, much easier.
There are several courses of action that you can take:
- 1. Contact the Army Corps of Engineers
- 2. Contact NARA regarding morning reports of this unit
- 3. Contact an independent agent for research
Of course the NARA Morning Reports route will take a bit more effort. You either have to go there in person and go through records or you can hire a research student to help you with your quest. NARA is having problems with their site this afternoon, so you may want to try again later today.
I can recommend a very good historian who runs his own research company. You can contact Richard at: WW2 Connections. He offers several levels of research that are dependent on how much info you want and how much you (or anyone else) are willing to spend. He is extremely knowledgable and has over 5000 books in his personal library.
Good luck to your friend. Keep the faith! 
Proud Daughter of Walter (Monday) Poniedzialek
540th Engineer Combat Regiment, 2833rd Bn, H&S Co, 4th Platoon
There's "No Bridge Too Far"