Yep, the cupcakes will be fine. As long as they are not cream cheese frosting (which if you are using a Rose recipe, probably not) they will be fine sitting out in a box. I have left cupcakes out at room temp, covered (but not necessarily airtight), for up to a day, and they are always good. I like the idea of wrapping a garbage bag around a large bakery box, for extra insurance. I would be careful about leaving the garbage-bage-wrapped box in direct sunlight though, since it would magnify the heat a bit.
My favorite way to keep cupcakes fresh and transport them is the Cupcake Courier, which is attractive, airtight and extremely sturdy (holds 36 cupcakes).
It works perfectly unless the icing and/or decorations are very tall (1.5-2” or more) another plus is that the cupcake trays are removable so you can use it for a a layer cake or pie as well.
If there are tall decorations, or I need to be able to drop off disposable boxes, nothing beats these sturdy clamshell muffin trays (I get them from my local baking supply store).
Scroll down on this link to “6 cavity cupcake containers & muffin container with deep lid” (Outer Dimensions: 9 3/8 x 6 3/4 x 4 ” Bottom Cup Diameter: 2 1/8)
I try to avoid using these plastic boxes, even though they are so handy, and recyclable. I just prefer something reusable like the courier.