Does anyone have any experience with this?
For instance, consider Subversion, Git, or Mercurial, and a typical Windows Forms form.
Whenever someone edits the form, for instance repositions a panel to have a different parent, sometimes the form designer code generator rearranges more code than just that panel.
Does anyone have any experience with how big a merge problem this is?
Admittedly, I'm just a one-man team (with git), but I don't think I've ever seen horrible problems. Maybe some manual merges from time to time.
To be honest, where I've really had problems is with the .sln files (see this question). A designer.cs file you have a chance of understanding and merging visually. Solution files are a total disaster... I've taken to just taking one side of a merge and then correcting manually afterwards..
How about running a few tests?
Yes, I tried to answer it here. Simply put, what we do is to have a "pre-merge" script in PlastiSCM (you could use it with your preferred SCM) to "sort" the resx prior to merge. This way we avoid weird issues.
Note: Delphi did a better job handling resources 15 years ago than the newest generation VStudio... :(