It might be a waste of money. Do the customers receiving your menu already have one from last time they ordered? Are there coupons on your menu that they can use to make keeping it worthwile? How recent is the menu you are putting on there - is it the same menu you have been using for a year, or one that is 2 months old? Do you change your menu appearance each time you reprint so that your customers notice that it is not the same one they got last time?
In some cases it would be a good idea to give your menu: I.E. ask your POS provider if there is a way to print NEW CUSTOMER on a receipt when you box up the order. Only give these customers your menu.
Or if you do print new menus, give one to everyone for a month, then taper it off.
You should seriously look into EDDM through the post office. You will have to make a few adjustments to how your menu is printed to fit their standards, but you pay for, bundle up, and drop of so many menus (appx 500-800 per route) per week to your post office. They mail them out to your specified carrier route that you chose. Mailing menus will get your menu in front of new customers every week. Start with what you can afford as part of your advertising budget.
Dan