A modified stat block is still a stat block
In summary, a modified stat blocks count as a stat block, too; polymorph as written does not limit you from copying an individual creature's stat block, so you could copy a modified beast, but it would be up to the DM if that process also copies things like equipment of the target.
The game refers to statistics and stat blocks (or character sheets) interchangeably
Polymorph itself never uses the term stat block, it says:
The target's game statistics, including mental ability scores, are replaced by the statistics of the chosen beast.
However, there is a Sage Advice Compendium entry that explains that the statistics refer to a stat block:
Can a creature under the effects of polymorph have other spell effects on them, or are those game statistics also replaced by the those of the beast form? Polymorph replaces only the target’s character sheet or stat block with the stat block of the chosen form. Other effects, such as other spells, still exist
The DMG (p. 92) further states:
When you give an NPC game statistics, you have three main options: giving the NPC only the few statistics it needs, give the NPC a monster stat block, or give the NPC a class and levels
So, having statistics and having a stat block (or character sheet) are interchangable. (It's another question what happens if you could turn into an individual NPC that has incomplete statistics, but I am not aware of an ability that allows for this. Presumably the DM would need to make something up in a hurry, or use Commoner stats or another standard stat block).
From the game's perspective, a creature has statistics, and those are recorded or formatted in a stat block (or character sheet). If you modify the stat block, the creature still has statistics, just different ones. You again could print them as a stat block.
There are also creature statistics that are not for individuals and that are defined in exactly this manner. For example, Tomb of Annhilation provides an actual stat block for an Albino Dwarf, but also defines Albino Dwarf Spirit Warriors like this:
An albino dwarf spirit warrior has the statistics of an albino dwarf warrior, except it has a challenge rating of 1 (200 XP) and gains the following additional feature:
Innate Spellcasting. The dwarf's innate spell casting ability is Wisdom. It can inn ately cast the fo llowing spells, requi ring no material components: 1/day each: hunter's mark , jump, pass without trace, speak with animals , speak with plants
While there is no actual stat block printed for these Albino Dwarf Spirit Warriors, this description is equivalent to having a printed stat block for them, that includes the Innate Spellcasting feature, it just saves space for more adventure text, instead of replicating nearly all of the stat block.
So, in principle if a creature has statistics, these can be represented as either a stat block or as a characters sheet, or as a reference to a printed stat block with noted modifications. For the purpose of a spell like polymorph, these are statistics.
What do the spells say?
However, if you can transform into something also depends on the text of the spell. There are many individual creatures that do have actual, printed stat block, for example the archlich Acererak in Tomb of Annihilation has a stat block. That does not mean you can turn into Acererak if you true polymorph yourself, because that spell says
If you turn a creature into another kind of creature, the new form can be any kind you choose
so you can only transform into a kind of creature with that spell, not into an individual creature.
Polymporph actually does not limit you to a kind of creature, it only limits you to a creature of beast type:
The new form can be any beast whose challenge rating is equal to or less than the target's
So technically, as long as it is a beast, and it has a stat block, or has statistics that define a stat block, it could be a target. You could argu that if Polymorph Any Object cannot do that, than the much weaker spell Polymorph should likewise not be able to do it, but the wording is different, and I can see DMs ruling like this, even if that is not what the text says.
You cannot polymorph into an individuum
I think that polymorph in any case is not able to turn you into an individual creature, just a type of creature. If you know the dog named Fetch that uses the mastiff stat block, you could polymorph someone into a dog with the mastiff stat block, but I do not think you could polymorph them into Fetch, the dog. Because the creature overall also has a spirit or a soul, that is not captured in the stat block, and that you cannot create by polymorphing.
Its not clear if equipment would be created
Does the True Polymorph spell form a creature with equipment? discusses if you can or cannot create equipment, with answers highly upvoted on both sides of the fence. Normal polymporph has this problem less often, because the normal beast stat blocks typically have no equipment, but could you polymorph, for example, into an armored mastiff, if you had seen such a beast, i.e. a mastiff in barding? The same goes for creatures that have been modified, for example by losing a limb. If you polymorph into that creature, will you have all the limbs? I think this is up to the DM. For my tastes, limiting to a kind of creature avoids all these issues, and is what I would do, but another DM might approach it differently.