Can I leave my cinnamon bars unbaked in the fridge for a few hours?

It will probably not affect taste, however, it will affect texture. The reason is that the flour will react to the moisture in the batter and start to convert to gluten. This will produce at best a chewier bar (which may actually be desirable) or, at worst, a rock hard bar.

If you are willing to take this textural risk, then I would recommend putting the pan directly into the oven from the refrigerator. This is because the bars will be so thin (and thereby have relatively large surface area) that they will come up to temperature in the oven quite quickly. You may have to cook them slightly longer; just make sure to test them with a toothpick or, better yet, a thermometer before removing. The internal temperature should be a little over 200°F or a little under 100°C.

If you want to minimize the risk of chewiness/hardness, do as little initial mixing of the flour with the batter as possible. It is okay to have some small lumps of flour since they will absorb the batter during the resting time in the refrigerator. This suggestion is due to the fact that gluten is formed both by moisture and mechanical agitation (mixing).

Another option, for which there is no potential harm, would be to mix the wet ingredients in advance and refrigerate them, also mix the dry ingredients in advance and leave them at room temperature, and then mix the wet with the dry just before putting everything into the oven.

The issues you will have holding a dough like this for several hours are:

1. Gluten development. This recipe is based on the creaming method, so the butter/egg/sugar emulsion will coat the flour particles, tending to inhibit gluten formation and toughness which happens over time, in the presence of moisture, even without mechanical agitation. For holding periods of just an hour or two, this should not be a terribly significant factor.

2. Leavening. This recipe is leavened by baking powder. Most baking powder will expend some of its power during the resting time, but will have a second (the double acting part) burst when the heat hits. This looks to be a fairly thick batter, so should not lose too much leavening. You may get a product which is a tiny bit denser due to this.

3. Hydration of the flour. Allowing the batter to rest will allow the flour to hydrate more thoroughly and the flavors to blend and mature. This may actually enhance the texture of the batter.

4. Crust texture. The extended rest time will allow sugars to more thoroughly dissolve which may give a more crispy, frangible surface crust development (somewhat like a brownie gets). This may be a positive, but if covered later with the glaze should not be noticeable.

5. Filling or swirl texture. During the hold period, the cinnamon and sugar swirl or filling will be in contact with the moisture from the main batter. This will tend to dissolve the sugar, and you may loose some texture and appearance from the swirl, but the cinnamon taste should remain.

6. Food safety. This is a batter with raw eggs. Make sure you put it in the refrigerator to prevent spoilage, and I would recommend baking it directly from the refrigerator to prevent having to rewarm it.

7. Baking time. If you bake the batter cold from the oven, you may have to adjust the baking time slightly.

All in all, this recipe looks like it should work if you hold it for a couple of hours, maybe 3-4 at the outside. I would not try to hold it overnight.

See also: What does an overnight chill do to cookie dough, that a 4 hour chill doesn't?