It's certainly possible, however it doesn't seem probable that Tarses would a grade lower than someone who isn't even an adult given that it's explicitly his third tour (and in most services you "rate" before or during your first) and a naval tour can be anything from six months to three years in the RW (licensed media suggests that Simon was 21-22 during The Drumhead, the actor who played him, Spencer Garrett, was 28 so clearly they wanted to imply some experience (and does correspond to the TIS for Senior Airman in USAF), whereas the...
I don't know what the relative ranks of Tina Lawton and Simon Tarses might have been about a century apart and centuries in our future.
What is the legal age of adulthood for Earth Humans in the era of TOS? In the 20th century it was lowered from 21 to 18 in the USA, and in some countries it is as low as 15. Furthermore, I have once read that military service grants legal majority, so possibly Tina Lawton could be a legal adult as a result of joining Starfleet.
Why can't someone be a grade lower in rank than someone younger in age?
I remind you that in the alternate universe in "Tapestry" Jean-Luc Picard found himself a lieutenant junior grade at the same age he was a captain in his normal timeline, so apparently it is possible for someone to have one or five promotions in Starfleet during the same time span depending on various factors. In that experience Picard finds that he is junior by two grades to Lieutenant Commander La Forge, who is only about 0.51 times Picard's age in "Tapestry".
And Picard never complains that this is a lie because it would be impossible for a Starfleet officer to go as long without promotion as he apparently did. Of course Picard doesn't complain that it would be impossible for La Forge to be a lieutenant commander at such a young age, because no doubt Picard himself was largely responsible for promoting La Forge to lieutenant commander several years ago and thus knows first hand that it is possible for an officer to be promoted that fast with good reviews by their superiors. Thus Picard must believe that Starfleet's normal promotion practices allow for both a 64-year-old lieutenant junior grade and a 33-year-old lieutenant commander.
And in "Datalore" Wesley says:
WESLEY: That everything that I have said would have been listened to if it came from an adult officer. Request permission to return to my quarters, sir.
And apparently it is within Picard's authority to appoint a 15-year-old civilian an acting ensign. And Wesley is put in charge of a team investigating unstable planets as early as the age of 16 in "Pen Pals".
As I remember, during the US Civil War there were a few "boy generals" who were promoted to brigadier generals and even in some cases major generals of United States Volunteers while still in their twenties. And the immediate subordinates of those generals in their twenties would usually have been in their thirties, forties, and fifties, possibly a few in their sixties.
One of those generals, Uriah Galusha Pennypacker, commanded a brigade as a colonel and then was promoted to brigadier general when his age in army records was about 25, I guess. However, it is possible that he was much younger than his age in army records, since sources give his birth date as late as June 1, in 1842, or even June 1, 1844. Thus it is possible that he may have been promoted to general age 20, when still a legal minor, and commanded a brigade age 19, which would make him years younger than most of the privates.
A close relative of mine was a sergeant in World War I aged 19, and his brother graduated from West Point and was commissioned a second lieutenant aged 20 years and about three weeks & thus had 11 more months to go before becoming a legal adult. And my research shows that he was not the youngest person to graduate from West Point and be commissioned a second lieutenant during the 20th century.
So I see no reason to believe that in Starfleet every single person who has a specific pay grade must be older than every person who holds the next lower pay grade and younger than every person who holds the next higher pay grade - and even if Starfleet members don't get paid in the TNG era they do get paid in the TOS era.