No, buying a cheap pearl for 100 gp doesn't work
The rules say "worth at least 100 gp", not "bought for at least 100 gp". If you buy a cheap pearl from another character for 100 gp, it doesn't become 100 gp worth. And vice versa, if you steal a 100-gp pearl for free, it is still 100 gp worth. This is true for any items, not only for material spell components. The item's cost is determined by a few factors, including the item's quality. So, the item's cost is a (very) rough equivalent of the item's quality. So, why the PH specifies the cost, instead of describing the quality?
Specifying a cost is much easier than describing a quality
Aside from the seller's insights, nothing specific makes an item worth X gp.
"Worth at least X gp" is a short, convenient indication of the item's quality. 5e PH does not describe any specific criteria of "worthing X gp" (hence, being suited for the spell) - it only says the item's guiding price, one number instead of a bunch of words. It's the DM who should decide and say "unfortunately, this pearl is too cheap and small to be used for this spell".
Let's elaborate the pearl example. Instead of "worth at least 100 gp" the PH might describe its minimum weight, radius, material, shape, surface quality, etc. PH had to describe such criteria for every single material component in this way, which contradicts the 5e paradigm. Instead, the PH just says "worth at least 100 gp" - so both DM and players get an idea, what kind of pearl it should be.
Your DM might go the easy way
It really depends on the playstyle, but a DM might decide that market conditions is not a thing in their world. Instead, he/she might take all the prices from the PH and use them as absolute prices, instead of guiding ones. Using static prices model solves many buying/selling questions, but in the end leads to hilarious absurdities as a downside, which might not be welcomed by players.
Yes, it can, for both RAW and RAF reasons.
It is worth at least 100 GP based on being an uncommon magic item which is valued at 101-500 GP (DMG, p. 129 & p. 139). It is a pearl. The spell component is not consumed in the casting.
(a pearl worth at least 100 gp) (identify, spell description, SRD)
RAW (rules as written): nothing prohibits its use.
RAF1 (rules as fun): why not allow it? That's a good use of assets by the players.
Bravo to your players!
1
RAF. Regardless of what’s on the page or what the designers intended, D&D is meant to be fun, and the DM is the ringmaster at each game table. The best DMs shape the game on the fly to bring the most delight to their players. Such DMs aim for RAF, “rules as fun.” ... I recommend a healthy mix of RAW, RAI, and RAF!
Best Answer
It probably disappears.
The rules for material components state:
So we know that when a spell consumes a material component, that component is no longer available to be used next time you cast the spell. The idea with material components (especially costly material components) is that you have to do the work to acquire the component for each casting of the spell. So suppose a 1000 gp diamond is "consumed" in the sense that its magical utility is gone, but it is still a 1000 gp diamond. One, the game nowhere makes this sort of distinction, rather it assumes that any 1000 gp diamond is suitable for spells that call for one, and two, we could just sell it for another 1000 gp diamond that has not been consumed, since the game assumes gems are "trade goods" and always able to fetch their value at market. The only reasonable conclusion we can draw is that "consumed" means the material component is gone, eaten by the spell, unavailable for spellcasting and commerce.