Is it recommended for a person in a state of ritual impurity (junub), if he stays overnight at a friend's house, to pretend to pray without having performed ghusl so that he is not suspected of fornication?

We do not know of any scholar who permitted prayer without purification when purification is possible. Intentionally doing so is considered a grave sin. If the worshiper intentionally does so, knowing about the impurity and the impermissibility of praying with it, he has committed a great disobedience, but he does not become an infidel by it unless he deems it permissible.

As for what your friend might be referring to, it is the permissibility of performing tayammum (dry ablution) instead of ghusl (ritual bath) for janabah (major ritual impurity) if one fears being accused of something or being slandered unjustly. This tayammum permits prayer, recitation, and touching the Mushaf (Qur'an). However, this is conditioned on a strong presumption that the accusation will occur, not mere delusion, and there must be an inability to perform ghusl without the knowledge of the one whose accusation is feared.

As for abandoning ghusl and tayammum out of shyness or embarrassment, it is absolutely impermissible. Performing prayer without ghusl or tayammum (where tayammum is valid) is only permissible in cases of lacking water and earth or being unable to use them.