OP, this is a great question that demonstrates you are really thinking about the dynamics.
I understand your question to be: for a given ambient pressure, with a given tissue saturation, if you vary the fraction of nitrogen in the inspired gas, does that change the pressure gradient (supersaturation) of the tissues, and therefore lead to an increase risk of decompression illness?
The answer is, to the best of my limited knowledge, no. In the Buhlmann models we use for calculating this, the supersaturation of the tissues is related to the ambient pressure, not to the difference in pressure between the partial pressure of the inspired gas and the supersaturation of the tissues. Bubbles form in the tissues directly, as a direct consequence (detail below) of the ambient pressure combined with how much gas is dissolved into the tissues (saturation) (and other factors). The contents of the inspired/breathed gas has no impact on the pressure of the gas you are breathing, or on the immediate likelihood of bubbles forming anywhere in the body, but it will change the dynamics of the diffusion of gas into and out of the blood. As an example of a diver descending, for a greater partial pressure of nitrogen in the inspired gas, then there is a greater rate of diffusion of that gas into the blood as you breath. Alternatively, there is an associated decrease in nitrogen diffusion rate given an increase in the fraction of oxygen in an inspired gas. This is why you can stay for longer at a given depth given a higher fraction of oxygen, as the differential pressure between the inspired partial pressure of nitrogen and the tissue diffused gas pressure (saturation) is lower than had there been comparatively more nitrogen in the inspired gas. A bad analogy is like drinking a cup of 5% alcohol (beer) vs. drinking a cup of straight 50% alcohol (hard liquor). You would need fewer of the 50% cups to reach the same level of intoxication, sort of how you need less time at a given depth to reach a similar saturation of nitrogen if the fraction of nitrogen inspired is greater. You ask specifically about ascending, and as above, the tissue saturation (amount of diffused gas at a given pressure) is dependent upon the ambient pressure, so breathing a higher fraction of oxygen doesn't lead to greater tissue saturation, but does lead to greater rate of gas diffusion out of the blood through the lungs and into the expired gas, commonly called off-gassing.
Good comments, and I believe that lostsheep has a nice answer which addresses your specific question. I apparently can’t help but digress way too far into the weeds.
First, characterizing the mathematical models that we use to calculate risk of decompression illness is one thing; and characterizing what exactly is happening in the body is another thing. The goal is of course to use mathematical models that are as close to reality as possible. While we know a lot, and are able to use that knowledge to dive safely, scientifically speaking, I tentatively believe as a layperson that the exact dynamics of the relationship between bubbles in the blood and minor decompression illness aren’t entirely understood. In simpler terms: decompression theory is complex and imperfectly understood, and one can dive deep into the science.
Bubbles. It’s important to note that I don’t think the Buhlmann model mathematically predicts bubbles specifically; it defines gas diffusion into and out of several “compartments” which are theoretically analogous to different types of tissues in the body. For example blood, and fat, which have different rates at which gas diffuses into or out. My haphazard and tenuous understanding is that bubbles are not perfectly correlated with symptoms of minor decompression illness, though they are indicators of decompression stress, and are always present in cases of serious decompression illness. Additionally, gas dissolves into and out of your body regardless of whether or not there are bubbles present. When the supersaturation of a tissue is large enough, i.e. the ambient pressure is way lower than the dissolved gas pressure in that tissue, bubbles will form, if the difference is small, bubbles will not form, and if the difference is in a medium range, they may or may not form. Keeping the supersaturation of a tissue compartment low enough is the primary method used to prevent decompression illness, which also hopefully prevents bubbles from forming. A huge part of dive training at every level is to give divers the ability to do this. The mechanics of bubble formation is complex, and there have been attempts to write decompression algorithms/models that incorporate this complex physics, though using those models is not popular today, as they seemed to be less capable of predicting decompression illness than the Buhlmann tissue gas diffusion compartment model. (If interested look up RGBM or deep stops, which I don’t use to plan dives)
In short, while preventing bubbles is a good way to think about and introduce the idea of decompression illness, but don’t focus too much on bubbles, focus more on compartment supersaturation if your understanding is at that level. Decompression illness is really what we want to prevent, and using more oxygen in the gas mix is a good way to do that, of course while keeping the risks of the oxygen low. Bubbles will be reduced in the process.
I can’t help but also bring up that there are other factors that influence all of these dynamics, from temperature, to probably physiology, to rate of pressure change, the list goes on… Also nitrogen isn’t the only inert gas out there. Good luck!
Please excuse my lack of brevity, and don’t trust what I’ve said without someone knowledgeable agreeing; please criticize!
