The answer to that is yes. Yes they do.
Have you missed the males with transgender identities posting their period pain and PMT videos on social media? They even have videos where they share recipes for ice blocks with a blood simulation that they insert into their anus or the cavity that they have had implanted into their body to melt and simulate a period. And that does not even include the sex fetishists who get used period products.
There are males out there that have declared that they are in menopause too. Or they get euphoric by receiving menopause check up invites (or Pap smears etc) and they publicly share this.
And there already have been male people who have simulated pregnancies, joined pregnancy forums and support groups and then simulated the delivery of a stillborn infant. And joined the still born infant support groups. There is constant discussion about when male people will be able to have implanted uteruses so they can experience pregnancy. AND get abortions as one very prominent male with a transgender identity publicly fantasised about.
Plus there are a growing number of male people who feed babies an untested secretion from their breasts. There has NEVER been a full and comprehensive test on the contents of that secretion for cross drug interactions. And as there is no receptors and the endocrine system is not set up to support the interaction between infant and that male person, there is no way the body is able to modify what is being fed either. In other words, this activity is purely based around the male person's desires and not about the infant's needs at all.
Once you see all this, it is very hard to unsee what is happening and what some groups are attempting to normalise. What is important however, is that it is an extreme sub group who do this. Not all males with transgender identities.