Depends on the type of people your players are and the kind of game you like to run.
If everybody wants to agree that everything happens in full dollar amounts, that nobody will play the stock market, no-one gets credit cards, etc etc, it would work out just like D&D or any other game that tracks full-dollar amounts in-come/out-flow.
Saying: "You have $1,000." "I spend $500 on a Glock 17." Isn't unbalancing in the least.
Wealth takes modern finances and does a few things with it:
It turns a complex interlocking system and boils it down to a simple value. Rent, clothes, gas, food, going-to-the-movies, are all accounted for. Job, account interest, trust funds, are all accounted for. The back-end is in the broad numbers.
It turns paperwork, down-time, and accounting into a dice-inclusive game system. Like a Will save or an Attack Roll.
The only problem I'd see with doing straight dollars is if you have a smart-aleck who decides to try running investments and credit cards and the like. But that same guy is going to try and find ways to bend the Wealth system, so, don't really see as either methodology is going to stop somebody that wants to be a problem.
For myself, 70% of my last D&D session was spent appraising, identifying, selling, divying, burning (several feats that can consume magic items for other purposes) ... re-divying, and buying magical items. We spent several days of "Game World Time" between shopping trips, but I still had the same 523gp 37sp and 25cp a few days later. We didn't take the time to buy ale or rations or feed for the horse. We're not going to take time calculating how many copper pieces a day my character spends on food or ale, but I have a copper-pieces line in my character cash page. I remarked then that I'd rather have rolled a few Wealth checks back and forth and had been done in a few minutes. Any sense of realism was ruined by that 25cp that have been there since 3rd level. Any sense of simplicity went out the window when we had to pull a calculator and scrap paper out to work the multiplication and division to do finances for 13th level characters.
The next time I run D&D, I'm going to use the Wealth system instead of tracking cp/sp/gp/pp. Last time I ran a fantasy game I used Wealth and it turned out well. YMMV.
--fje