Yes, it is very dependent on gluten. You cannot get the typical texture of a classic bread without the gluten of wheat flour.

If you have to bake gluten-free, you can do some limited yeast baking by using a gluten-free flour in combination with thickeners, such as guar gum. The achievable textures are close to the cottony white loaves introduced by American industrial production (I've forgotten their English name, sorry - in Germany they are called "bread for toasting").

The flours you use for this have to consist of starch - so you can use rice flour, but not something like defatted peanut flour. Also, the process for this baking is so finicky that it almost doesn't pay to experiment, unless you are very determined and are willing to live with a failure rate close to that of drug development. Instead, you should follow published recipes to the letter for this branch of baking - it is difficult enough to get these to work.

Yes, rising is very dependent on gluten. In almost all cases, you won't get any rising without a gluten-rich flour. Even if you use wheat flour, but one that has the wrong proportion of gluten, you will get a disappointing rise. If you were to try making a bread recipe calling for AP flour (8-10% gluten) with bagel flour (14-15% gluten) or a recipe for bread flour (12ish percent gluten) with pastry flour (6% gluten), one prominent problem will be very little rising.

I said "in almost all cases" and not "in all", because some clever people have found limited ways to get rising without gluten. The limitations of such baking are:

• you can't achieve most traditional bread textures with this kind of baking. You only get bread that resembles the cottony, light bread with soft crust that is the prototypical bread in an American supermarket.
• you can't use any gluten-free flour. What you need is a flour that is almost pure starch. Rice flour can be used to make a gluten free bread recipe, defatted peanut flour won't work well.
• You have to use something to replace the gluten, typically a combination of thickeners like guar gum.
• It is a very finicky process. Making up your own recipes by experimentation will have an immense failure rate. Instead, you should follow existing recipes to the letter, and live with the fact that you will need quite some exercise to learn to execute them well, if the recipe was any good to start with.

So, if you manage your expectations and invest some time in choosing and learning a good recipe, you can get risen gluten-free bread of a certain type. In that sense, yeast bread doesn't strictly "require" gluten to rise, but for most practical purposes, the answer is quite close to "yes it does".