The idea of invisible cash shop is twofold:
1.It introduces the idea there is no separating barrier between paying/non-paying users.
2.It allows in-game access to everything sold by the cash shop.

How its done:

A.Company only sells in-game currency. Typically vast sums(millions of gold) for a few dollars or even less.

B.Game contains NPC vendors which have a "premium/luxury" page with items listed with exorbitant prices(in the game currency): most players wouldn't be able to afford them. These vendors are normal NPCs with no special idea of them selling "cash shop stuff".
More advanced systems would disguise the exorbitant prices with multiple in-game currencies, with "cash" items sold with more rare currency or resource.

C.Players begin to farm in-game gold to get these premium items: but there is a shortcut to buy gold directly from the company, saving them plenty of effort.

Result: dedicated players farm gold, others buy it. A vibrant economy based on in-game currency allows these items to spread and be auctioned/traded again.
However players will eventually discover this system and will understand its pay2win component if items sold are gameplay-breaking: see for ideas ).

The main effect of "invisible cash shop" is inserting cash shop items into the main economy: players have at least the opportunity, however small to eventually buy their favorite "cash item" without spending real money(however this is going to be much harder and longer than buying gold: since gold in such a game would be much scarcer).

In-game currency: The sources of currency in-game have to be balanced and not allow such things as allowing magic modifiers to increase currency/resource drops from monsters/chests(or at least have a hard cap to the modifier).
Anything sold to vendors also have to be limited in price: randomly-generated items should not have high sell prices.