Sort of and absolutely! The wedding cake is a wedding tradition, makes a great photo-op and is a showpiece/centerpiece for the reception. After the wedding dress it is the most popular item at the wedding guests want to see.
If a large tiered cake isn’t for you order a small three-tiered cake and cut it for the tradition of it and then either serve a sheet cake or another dessert you like.
If you just don’t want a cake at all then don’t have one and serve your guests any dessert that will complement the main course.
Another options is to create some type of dessert buffet -- bakery bar, cookie bar, ice cream sundae bar, pie bar or candy bar, though a bar candy is more as a treat or for guests to put in a bag as a wedding favor.
As for a tier of cupcakes, ask the baker if they can make an extra large cupcake for the cutting ceremony or cut into one of the ones on the tier.