The plan should not work due to the word game being played
You are inflicting something like progeria on the young dragons
Growth and maturation, and aging, are not direct synonyms. (Example: I have never stopped increasing in age, but I stopped growing taller in my mid to late teens, and I was full grown/developed somewhere in my early twenties).
The connotation of "growth" is positive - there's more to it than a numerical ticker. In the description of ghost's ability, "aging" is negative effect. It is a debilitating effect. (see below)
(MM. Ghosts) If the save fails by 5 or more, the target also ages 1d4 × 10 years. (snip) The aging effect can be reversed with a greater restoration spell. (Basic Rules, p. 129)
It takes positive energy, greater restoration, to reverse the negative magical effect of aging.
If the BBEG tries to age baby dragons with a ghost, you could expect them to die prematurely (life expectancy for progeria is somewhere in one's teens) rather than to grow into their next phase of maturity. Growing into maturity is a gradual process that over time (and by eating a lot of Pyrena's Red Dragon Chow, or someone's livestock) sees the dragon develop into it's next size and power level.
Why can't the ghost's aging be beneficial?
Firstly, because it is overcome by the greater restoration spell.
(Basic Rules, p. 96)
You imbue a creature you touch with positive energy to undo a
debilitating effect. You can reduce the target’s exhaustion level by
one, or end one of the following effects on the target:
• One effect that charmed or petrified the target
• One curse, including the target’s attunement to a cursed magic item
• Any reduction to one of the target’s ability scores
• One effect reducing the target’s hit point maximum
And, per the ghost ability's description, ghost-inflicted aging if cast within 24 hours.
Secondly, consider the basic premise of who is adventuring in D&D 5e (and thus who will be aged by monsters such as a ghost): it isn't children, it is player characters. Player characters are presumed to be mature members of their race/species, from young adults to full fledged adults, and possibly old adults, who got the urge to adventure1 (Sage background, for example).
- A tree grows for centuries, a human for a few decades, and a dragon somewhere in between (though more toward the tree). A dog born on almost the same day as my son matured and died before my son got out of puberty.
The PCs have stopped growing and maturing, thus a ghost aging them (in the negative sense) accelerates their approach to death and / or disability (aside from a few class/sub class features like the Druid's timeless body).
Aren't exploits part of the fun of D&D? Sure they are.
Since you are the DM, you can do as you like and are not bound by any RAW in the first place. (Such that I wonder why you asked the question, but thanks for asking since it got me thinking! 😃 ) What you have proposed is an overly-complicated means to an end, which is to throw a "gotcha" at your players when they are out saving the kingdom / region / villages from a bunch of marauding young dragons. (A common enough malady in a D&D campaign).
Review your purpose in doing that:
- Firstly, why do I want my characters to believe that they just killed some children? Is that really how we have fun at D&D tables? At some tables, yes, that is within the group's boundaries; horror is an element in any number of TTRPGs.
- Secondly, how do I provide clues?
What plans do you have to provide a form of subtle cuing that "something is not right" before the on / off switch of "dead dragon reverts to the form of child" hits them in the face? See the Alexandrian's "three clue rule" for some guidance on that.
@CaptainMan made this suggestion, for a clue on weird magical things going on: at some point the party finds "old baby dragon" skeletons in an evil wizard's lair that were the result of an attempt at this scheme
- Lastly, consider the Villain's effort versus capability
If the BBEG can cast 9th level spells, is this solution the best use of his / her resources? Granted, this scheme you propose fully fits into the cackling evil villain trope; BBEG's being purely evil is very much expected. @Rubiksmoose offers a more efficient alternative, though it may not give you the horror element that you are looking for.
While you can do as you wish, this answer is intended to provide an alternate view of both growth and aging than as game mechanics to exploit, and recommends going into a little more depth in providing your players a challenge, however horrific you choose to make it.
The other contributor to this answer is the points made by the devs for this edition regarding the default to plain English interpretations of the rules text.
1 (Backgrounds, PHB, pp. 127-141, describe most professions as what the character has done 'for years' before choosing a life of adventure; Guild Artisan, Soldier, Sailor and Sage in particular)