Polymorph refers to a beast's given statistics
In summary, modified statistics are statistics; polymorph as written does care about statistics, not stat blocks, and does not stop you from copying an individual creature's statistics. So you could copy a modified beast, and it would be up to the DM if that process also copies things like equipment of the target.
I'd like to be up front that this feels off. It feels like you should not be able to copy an individual's statistics with polymorph, just the underlying "base" creature statistics that are expressed in the base creature's stat block, and that is how I would rule it in my games. But the actual rules text does not support that intuition, so this will be up to the DM.
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.
For the purpose of a spell like polymorph, what counts are the creatures statistics, not if it has a formatted stat block.
The Monster Manual says on page 6:
A monster’s statistics, sometimes referred to as its stat block, provide the essential information that you need to run the monster.
It then goes on to list the elements of the statistics. This says that a "stat block" is a way to sometimes refer to a monster's statistics, but what counts are the statistics. Most of the time, having statistics and having a printed stat block (or character sheet) are interchangeable. If you modify the statistics, you modify the thing that polymorph can target.
From the game's perspective, statistics are recorded or formatted in a stat block (or character sheet). If you modify them, you again could print the new ones as a new stat block. Or you can record them as changes to a pre-existing stat block that you reference.
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 innately cast the following spells, requiringno 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.
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. You could transform into an Albino Dwarf Spirit Warrior, but not into Traxigor, a CR12 level spellcaster that also is a tiny beast (from Baldur's Gate, Descent into Avernus, kudos to @ThomasMarkov for finding this).
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 statistics, it could be a target. You could argue that if Polymorph Any Object cannot do that, than the much weaker spell Polymorph should likewise not be able to do it, and I can see DMs ruling like this, even if that is not what the text says.
Note that playing it like that and being high enough level would allow you to transform into Traxigor. A DM who dislikes such an outcome could limit the spell to just general kinds of beasts.
It's 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, so I think this is probably best left to the DM to decide. Normal polymorph has this problem less often, because the normal beast stat blocks typically have no equipment, but could you polymorph, for example, into an armored sabre-tooth tiger, if you had seen such a beast, i.e. a sabre-tooth tiger in armor (like the one in Curse of Strahd)?
For my tastes, limiting transformation only to a kind of creature avoids these issues, and is what I would do, but another DM might approach it differently.