It is possible for a plotter using a real pen to make a card which is indistinguishable from a truly handwritten card.
People are rightfully squeamish about sending out cards which “look” handwritten but aren’t. Imagine a customer realizes that you are faking it…the consequences to reputation could be substantial.
That said, I personally find printed cards using handwritten-style font to be insulting, so that was a no-go for us.
We considered using a third party fulfillment service and essentially charging a fee on top of that, but the returns would be microscopic for the effort.