You will see players with higher ACs much sooner than usual because they will be able to afford full plate much sooner. Otherwise, you shouldn't have too many issues. Even with full plate, their ACs will cap around 20-22.
I'm not sure what your experience with 5e has been thus far, but I feel like it has taken a more nuanced approach with regards to player wealth. While it's accurate to say that lower-leveled players will have less wealth than higher leveled ones, players are able to break the game a lot less easily with wealth alone in 5e. Much of this stems from the fact that the primary means of power progression in the game stems from class abilities and constraints on magic items upsetting the bounds that a d20 can roll for the players.
Things that could tilt things out of control quickly are magic items given too early. Because players can't just expend wealth to create magic items, the ability for wealth to upset your game's balance is much more subdued.
That said, you may find that your players are purchasing plots of land or buying buildings with that sort of wealth. I'm not sure that's really a downside, it keeps them invested in the world, while letting you decide whether that land ownership does anything with regards to balance.
So to answer your question directly, no I don't think you have to. It will just make the players more wealthy, but not really impact the combat balance of the game. A 22 AC is hittable even at 1st level.
Not exactly a technical answer, but I hope it helps.
Disclaimer: This answer does not account for those players that elect to buy absurd quantities of chickens for some convoluted method of clearing out goblins.
FYI, page 38 provides the sort of wealth by level guidelines for the game, but you'll notice that they are much more vague compared to 3.5 where everything was measured in gold. Can't speak to how AD&D handled wealth.