Would it be a common thing for a man who had recently hired a female servant to have her virginity tested medically in the Victorian era?
No. Vehemently, absolutely no. Did you come across someone claiming this somewhere? Or is this a question intended to inform pornographic fiction?
Virginity testing was not a widespread thing in Victorian England. Obviously, the thought is titillating in the same way that the thought of the mythical medieval ius primae noctis is: ooh, the delicate young girl, the much older man, her unwillingness and innocence, the use of the law/medicine to cloak prurient interest ... At least the concept of the droit du seigneur is a widespread myth, though; this seems like something original.
Did doctors sometimes examine women to see if they were "untouched"? Yes. Famously, Effie Ruskin underwent a physical examination when she was petitioning for an annulment on the basis that her husband had never slept with her over the course of their marriage, because he would not come forward and corroborate her story to the court. There were times when it was felt to be important to ascertain virginity, as in a legal case that rested on it, and there was a common belief in virginity being easily discerned by checking for the presence of the hymen, but Victorian doctors were generally against this (though they did believe in some physical signs of sexual activity which did not distinguish between self-pleasure and sex):
[...] does it look well for those enjoying the light of civilization to so far imitate [a supposed African custom of showing a bloody sheet at the wedding] as to require an unbroken hymen as an evidence of virginity? Physicians know it is a very fallible test of virginity; that the hymen is often ruptured by various accidents; that cutaneous eruptions near the labia many times exist of such an irritating nature that the hymen is broken by the incessant scratchings of the victim; that the hymen is often destroyed by surgical operations in childhood; that sneezing, coughing, violent straining, and any number of other causes may break it; that the test is in fact no test at all, and only subjects those who happen to have the hymen broken to unjust and cruel suspicions. It is only a few days since I was called upon to examine a little girl, only seven years of age, whose hymen had been destroyed in consequence of an irritating eruption on the labia, causing her to scratch and frictionize the parts even in her sleep, and I could mention many other instances coming under my observation in which the hymen had been destroyed by the same cause or by accident. Why then preserve the hymen? Why regard it as an evidence of virginity when such a test only excites mortification and a sense of disgrace in a large proportion of all young females, not a small number of whom have always been chaste and unexceptionable in their character. Besides, the mortification of a broken hymen only falls on those the most innocent, and such as have become the least acquainted with the vices of the world. [...]
In asserting that the hymen is a cruel and unreliable test of virginity, I do not stand alone. Every intelligent physician, particularly in extensive practice, knows the fact, if deference to popular prejudice leads him to conceal it. But many have freely proclaimed it. [Quotations from other doctors follow.]
[...] I cannot but regard that [whim] which leads a young husband to suspiciously and sneakingly seek to know if his young bride has an unruptured hymen as humiliating and degrading to all the nobler attributes of a moral and intellectual being.
In any event, the woman of the house was the one who was meant to be doing the hiring of maidservants. If an unmarried man were wealthy and had a large estate, his housekeeper or resident female relative would manage it; if he were not and did not, he would be reliant on whoever his landlady hired to clean or on a charwoman who came in on a regular basis but didn't live with him. Employers did not own their servants, and while having a lover when she had been forbidden one could lead to a maid's dismissal, they did not have the right to force them to get invasive medical examinations prior to hiring.