Contemporary research is possible
There are a couple groups which could contribute to this line of research: Male to Female and Female to Male transsexuals.
MtoF transsexuals are castrated in the process of Gender Affirmation Surgery, which very rarely happens before the age of 18, and is preceded by some time of chemical testosterone suppression. (Some transsexual children do manage to avoid having the wrong puberty, but they are still a very small number, compared to the thousands of post-pubertal transitioners. Of course there is the complication that Gender Affirmation Surgery has only been really successful for about 50 years, so morbidity figures can't really be compiled with any degree of accuracy yet.
Looking at the other side of the equation, there are FtoM transsexuals who start taking exogenous testosterone, again usually post-puberty.
By examining these populations, we could get a much better picture of whether or not testosterone has deleterious effects.