Hi Minnesota,
Your cycling will stand you in very good stead and you should keep it up. I always say to regard exercise as mandatory when on hormone therapy - it has a beneficial impact on several of the side effects. You should also add some exercise to stress/shock bones, which cycling doesn't do.
I did buy myself a noseless saddle, although being noseless wasn't the main property of it, it was having a hole under the perineum and making sure you are sitting on your sit bones (pelvis) and not your perineum.
Both the hormone therapy and the radiotherapy will tend to reduce your hemoglobin level, but as a cyclist, you will have plenty in reserve, and you may not notice (unless you're racing or time trialing). Those without much in reserve get very fatigued at the end of radiotherapy. There's no research to show why this is, but I strongly suspect it's because their hemoglobin levels dropped below normal at that point.
You describe neoadjuvant hormone therapy (before treatment) which is usually 3-6 months, and concurrent hormone therapy (during treatment). However, it usually continues after radiotherapy (adjuvant hormone therapy), to make up a total of 1-3 years hormone therapy. You will need to exercise to maintain muscle (for which cycling is good), and to maintain bone calcium (which needs an exercise which stresses/shocks bones).