It can be shaped into a functioning (if disturbing) plan
Do note that, as a DM you are capable of simply giving the BBEG some random artifact or blood ritual that allows for this plan to happen. The following suggestion simply tries to make it fit more tightly to game mechanics and official spells / fluff.
First off, about the assumption of dragons hatching with a CR of 0. That simply is not the case. Although there is no current book on dragon Physiology and aging cycles, this information hasn't changed much since first it was released in previous editions. I'll quote a bit from the most current [4e's] Draconomicon on Chromatic Dragons, Page 13:
When a wyrmling is ready to hatch [...] [it] breaks free by clawing at the sides, pressing against and cracking the shell with brute strength, and blasting the shell occasonally with its own already developed breath weapon.
A newly hatched dragon has a full array of ablities. Although inferior to those of a young dragon these ablilties are sufficient for the wyrmling to take care of itself, at least against relatively weak threats and predators. Although an emerging wyrmling's sodden and somewhat awkward, it can run within hours of haching and can fly within a day or two. A wyrmling's senses are acute and [...] it is born with a substantial amount of its parent's knowledge imprinted in its mind [...] [and] the generalities of the world and its own identity.
The second they are out of their shell (or in that very state from polymorphery) the wyrmling is a threat to any ordinary peasant. It may suffer from a lack of coordination, but a breath attack is still a breath attack. As @Rubiksmoose and others said in their answers, the children in their "pure, natural" forms will not do you much good as polymorph fodder-unless you prepare your ingredients a bit, of course.
One approach to turning children into creatures powerful enough to be turned into dragon wyrmlings would be bonding them with demons, preferably Succubi / Incubi. That way you can create an army of tiny charmed (long-term charmed as per 5e fluff, not just the spell) Warlocks doing your bidding and growing more corrupted / powerful up to a level where they can become more worthy of your BBEG by willingly turning into a baby dragon and even more willingly embracing the horrifying gaze of your ghosts to grow big and strong (assuming maturing goes hand in hand with aging). A brainwashed, obedient Dragon seems a lot more useful than a frenzied murder machine that will literally just destroy everything around it.
A few pros to this approach:
- Little to no losses in the ghost and minion department (Each ghost of yours can be "killed" within at least 3-ish attacks at the wyrmling stage, even faster at later ages)
- Them dragons can be used much more precisely (if your BBEG rolls that way. If not they can still go haywire wherever he pleases of course)
- The succubi/incubi needed for indoctrination and pact shenaniganerry can visit villages at night and coax children into running into the forests for easy pick ups
- While you wait for their pact with the demons to grow strong enough you have a tiny army of hellmages at your disposal
A few cons:
- You need obedient succubi/incubi
- Indoctrination takes a while (may require a certain personality type)
- Empowering takes another while
- The dragons may be coaxed into betrayal if they retain (most) of their sanity
The largest (potential) con:
In my overall roleplaying experience (14 years of free form rp, 6-ish years of tabletop experience), most people have a special intolerance towards watching children being harmed, let alone actively harming them. Having your player fight some vicious creature only to find out it was, in actuality, a helpless, tortured little child could potentially scar sensitive players. Before embarking on such a disturbing plot you better be damned sure they are fine with it or can at least take it (either through a survey of Do's and Dont's to be done pre-game or anywhere before a big plot thing may happen, indirectly asking them what may be "too much" for them in their campaign or flat out asking them). Having a happy-go-lucky jokes galore campaign suddenly turn down such a grim alley may upset players in one way or another. Such things can end up breaking games and some people's love for the game.
One last (honestly tiny) issue:
Depending on how you interpret it, a permanently true polymorphed creature will not change back into what it used to be originally, its remains staying that of what it had been just seconds before it was killed. It's a tiny point you can easily rule to function as you wish it to, but some rules-lawyery players may try and fight you on that.
With some adjusted steps it's readily achievable. Your players may not be all too happy with what you made them do though.