Voltaire and one of the other statesmen of the day both attest to the injury. According to another Prussian person-in-the-know, it was due to a venereal dissase that Fritz had contracted (one posit is that he caught it on a visit to Dresden).
Grumbkow tells of an interesting story shortly after the Katte-Affair. Fritz was under house arrest at Wusterhausen. He was involved with a Colonel de Wreech. Or...to put it more correctly, Madame de Wreech. In due course, the madame became pregnant and tongues wagged. Friedrich Wilhelm sent Grumbkow to investigate, Grumbkow asked about the rumours, Fritz simply said "Untrue" not "kid's not mine" (but Grumbkow never mentions WHAT rumour he asked Fritz about. Is she pregnant? Is it yours? Are you having an affair with her? Is there a sordid little menage à trois à la Gustaf III going on? Or any of the countless other possibilities).
But then there's the reaction when the baby is born. It gets passed off as Madame de Wreech's husband's, but is never included in the official lists of Wreech's kids. This COULD be because the child only lived a few weeks (its not specified what gender the child was), but the most telling is from Fritz himself. A letter of six years later Fritz writes of it, calling the child an "adorable person, a little miracle of nature". He remains "attached" to Madame de Wreech, sending hrr his portrait and hoping she wouldn't think badly of him. When her property at Tamsel was damaged in the WotAS, he paid for the repairs himself.
Maybe Friedrich simply never got over the pain of the child dying?
As to his relations with his OTL wife, they were stiff and stilted because he regarded her as an Austrian spy. He himself wrote to Wilhelmine that "there can be neither love nor friendship between us. I will keep my word and marry the lady (Elisabeth Christine); but then it will be bonjour, Madame, et bon chance! My mute lady has sent me a china snuff box as a present. It arrived broken. What good can that portend?"
Ergo, if we acknowledge any of the above as true, Fritz is capable of fathering a child and forming an affectionate relationship with a woman. None of his siblings were heroically fertile as their mother (Philippine Charlotte more the exception than the rule; since Wilhelmine had one, Ansbach had four, Schwedt had five (of which two died), Lovisa had five; his oldest brother had four; Henry had none and his youngest brother only fathered the future Princess Radziwill, the rest of his kids' being fathered by his wife's lover).