Yes, False Focus can be used to replace multiple material components in the same spell, as long as the total cost is below the cost of your divine focus.
This is shown in the example in the rules text you quoted (emphasis mine):
By using a divine focus as part of casting, you can cast any spell with a material component costing the value of that divine focus (maximum 100 gp) or less without needing that component. For example, if you use a silver holy symbol worth 25 gp, you do not have to provide material components for an arcane spell if its components are worth 25 gp or less. The casting of the spell still provokes attacks of opportunity as normal. If the spell requires a material component that costs more than the value of the divine focus, you must have the material component on hand to cast the spell, as normal.
In the bolded line, it uses the plural "material components," indicating that the divine focus can be used for multiple components.
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.
Best Answer
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.
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!