Not if you build enough roads. This argument just does not hold up. There was less time wasted stuck in traffic in the past. Go with tunnels underground so as not the create the large problems with having surface roads. If your idea theory is right, why don't we just stop maintaining all roads, shut them down, and save a lot of money, if new roads are useless.
In some cases it might be theoretically possible to just outspend the problem. But in most cases the roads have to be going somewhere, and you don't have significant control over where and how big that somewhere is (i.e. you can't easily move a whole urban center, or slice it into chunks and move all the chunks apart from each other a little to fit more roads). If all the roads are ending at the same place, making wider and longer roads to that place will (often) just induce more people to drive to that place from further away.
The reason "just shutting down all roads" doesn't make sense is that it doesn't solve the actual problem, which is that people want to both work in places with good jobs (traditionally often dense urban centers) while living in cheaper places that are far away and not spend significant chunks of their lives stuck in traffic. Shutting down all the roads only "solves" the traffic problem in a deliberately ridiculous sense (same as "just kill all humans").
Shutting down or tolling chokepoints lowers the opportunity cost of alternatives.
I work for a big central business district employer. You can pay $150-250 a month to park or $75/week to take a motor coach bus from your suburban town. Those numbers drive behavior, and make for a better solution as folks who need flexibility can pay for it.
