I have done something to this effect multiple times. The first time I did a little drawing of my patrons if they wrote something I could quote about why they became a patron. I got one new patron that month who participated. Didn’t cost me anything, but a little time to draw up a picture.
At the beginning of the year I did a postcard set, thinking that maybe a physical reward might be more effective. It was rather unsuccessful and it was one of those things where I bit off more than I could chew. I started work on a 14 postcard series. At the time I had a monthly postcard reward tier for $10. For the promotion, anyone pledging $1 would get their choice of the postcards (the $10 reward) and anyone at the $10 level would get the entire set. It was literally the first month I didn’t get one new patron. I extended it for 3 months and only got one new $1 patron during that time who has chosen to not receive rewards. My current patrons were excited about the reward, but I just didn’t get any outside interest to speak of.
I did another when I had my Patreon anniversary and offered a choice of 2 posters to anyone who joined (and all current patrons of course). I got two new patrons, one who chose not to receive a reward. You’d think I’d learn, but I have another promotion going on right now for the first 100 people who become patrons. I’m nothing if not determined.
All in all, I’ve had very little success with that, but I also don’t have much of a social media following which contributes greatly I’m sure. My $20 and $25 patrons both told me they don’t support me for the rewards, but so that I can do my art. The patrons I do have are the real deal. I think you have to have a pretty good size following to make something like that happen. I suggest whatever the reward is, make sure it’s not something you have to buy in bulk (like postcards ) so that if you don’t have a lot of response, you’re not out too much.