It will be part of your medical records. If you are paying for it out of pocket (which by itself may be a red flag for the insurance company) it won't change the diagnosis of hypogonadism that caused the doctor to prescribe the HRT in the first place. For the most part, insurance companies are going to look at this intitially, not how much you are paying for HRT. Since you are paying out of pocket for yourself, you are automatically in a higher rate bracket. Just be aware of that.
The thing you need to have is a letter of credable coverage if you switch insurnace companies. The new company can request all of your previous medical records and they can do a search for them based on who your previous insurance provider was. They get super stupid if you don't have proof of insurance within the last year before switching companies. They can deny coverage of some medications, but by and large things like Insulin or other antidiabetic drugs, hormonal therapies, etc will be covered, you will just have jacked up premiums.