If you use the foamcoare letters, I would pre-drill the hole for the dowel before you cover/paint/decorate the letters. Then just pop through that layer before it dries, it would making string them on so much easier! As for support under the letters, I'm a better safe than sorry gal, based on the pics, the largest letter will be sitting on the support, so it probably won't be showing very much. And you can do what they did with the hearts and decorate around the base with some fondant/gumpaste decorations to hide it. My major concern would be keeping that dowel straight so the letters don't start to lean one way and end up taking part of the cake with them. The foamcore won't be very heavy, but if you cover them with fondant, they will have weight to them. If you decide to spray paint, it would keep them much lighter and you might not need the support underneath, and they wouldn't be touching the cake bc they would be resting on the plastic separator plate. I'm going to paste the pic here so if anyone has other suggestions for you, they can see the look you're going for.
Post pics when you're done, it's an awesome idea! :)