The free hormone hypothesis says that free testosterone is what matters, not total, and there is some evidence supporting this. My thinking is that it may be safe to assume this as long as SHBG is not too low. Some complications arise because SHBG has a role in androgen signaling that's independent of storage and transport. It's also been suggested that SHBG can enhance intracellular androgenic activity.
SHBG matters in your question because total testosterone is determined primarily by free testosterone, SHBG and albumin. This prevents us from saying that arbitrarily low total testosterone is fine as long as free testosterone is normal, because this in turn implies arbitrarily low SHBG, which may lead to some problems. In other words, total testosterone can be viewed as a proxy for SHBG, so you don't want it to be too low even with normal free testosterone, because that implies low SHBG and its attendant issues.
On the other hand, one can apparently develop and function without SHBG, albeit non-optimally:
We have identified a family with a missense mutation within the SHBG gene, which results in a complete deficiency of plasma SHBG in the homozygous state. Although total T level was low in the male patient, it did not interfere with normal gonadal development and spermatogenesis, suggesting a limited role of SHBG in sexual maturation and male physiology.
[
R]
