Hey Mark.
Being an author who is fairly well known in my own area of Nova Scotia - although less well-known anywhere else - I am often asked to read and/or talk and/or tell stories at local public events. Earlier this week I spoke at a men's homeless shelter. Later in May I am going to speak at a workshop being put on by myself and the editor in chief of a local publishing company. We will be talking about the various ways that a person can publish their manuscript - basically an indie versus traditional discussion. We expect a crowd of about forty or fifty folks. It is being held at our local Writers Federation.
I would NOT have considered handing out my card to someone at the shelter. They have got enough on their minds without me asking favors of them.
HOWEVER, if I was running a campaign next month I might very well hand out a business card with nomination information at the workshop - just because the people attending that workshop are writers and readers and folks who want to learn about the industry. These are people with a vested interest, people who actually paid money to come and hear me talk.
So you have to pick your targets wisely.
You might hand them out at work to folks who ask you about your writing, especially if you have worked their a while.
You might hand them out to your relatives, making it easier for them to help you out with a nomination. Heck, they might very well be honestly interested in what you have come up with.
It is a call you have to make.
Would I hand it out to a total stranger?
Probably not - unless, as I said, the situation lent itself to such an exchange.
How can you tell it works?
I can't really think of how you could easily tell if it worked or not.
In my opinion - at this point of the game - I probably would not bother printing up cards unless you had a LOT of people in mind.
I'd save my money if I were you. Find free ways to support your campaign. And remember, at the end of the game it REALLY isn't all about those orange H&T bars on your Kindle Scout Campaign page. The gods of Kindle Scout want a good salable novel in a good salable genre, hopefully with an author who has already established a good salable sales history.
But even then - you ALWAYS have got a shot.
Good luck and have fun. I'm putting you on the list.

PS: Here's a look at the business I do carry in my wallet. I've got a QR link to Kobo, just because I mostly hand these out in Canada, a Kobo-friendly country.
