While long-term study is lacking, one case study suggests that tucking can affect fertility.
In a case study  of one transwoman, tucking resulted in oligospermia – an abnormally low sperm count – affecting fertility. Elevation of the testes because of tucking may contribute to heat stress and consequent impairment of spermatogenesis.
After cessation of tucking and the provision of a new sperm sample, the sperm count in the patient was improved, and the semen had increased opacification.
A further study  found that tucking could create a suboptimal environment for spermatogenesis.
 Trussler, J. T., & Carrasquillo, R. J. (2020). Cryptozoospermia Associated With Genital Tucking Behavior in a Transwoman. Reviews in urology, 22 (4), 170–173. [Link]
 Debarbo, C.J.M. (2020). Rare cause of testicular torsion in a transwoman: A case report. Urology Case Reports 33. [Link]