OK, the answer is "Yes, there is control over it", but in reality not enough!
Using the following Citect.ini parameter you can specify the RGB value, but unfortunately you can't set it to transparent!
[AnmCursor]
Colour = 0xFFFFFF
The default value, 0xFFFFFF, is white. As I have a selection of light and dark background pages, I'll have to settle for the least annoying option.
Iain