I read a crappy business book citing the House of Orange as "branding" carrots. Don't ask, it was a terrible book. After doing a bit of googling, it seems there's a widespread understanding of a connection between the orangification of carrots and the House of Orange, but not a lot of hard evidence.
So why, exactly, did orange carrots catch on to such an extent? Surely someone outside of Holland wanted to continue growing purple carrots?
This is not a direct answer, but as far as I can tell, all articles that mention this either (a) do not provide any references or, (b) cite Simon Schama's Patriots and Liberators. I do not have access to a copy, and I do not really know Schama beyond this one badhistory post.
So that was a long winded way to say that my gut feel says this is apocryphal.