Yes, on a Mac with a new processor that is expected to be released in the latter half of 2020 (tentatively called the "next generation Mac"), iOS apps can be used as they are. The apps you are currently using on your iPhone are displayed as independent windows on the large desktop of your Mac, and you can operate them as if you were using a Mac app.
The current Mac (macOS Catalina) also has a mechanism called "Catalyst" that moves iPad OS apps on Mac, but it does not mean that iPad apps distributed in the App Store can be run on Mac as they are. Since it is necessary to rebuild (compile) the existing iPad application from the source code for Mac and optimize the screen layout, it is essential to support it at the developer level. Although most of the materials can be used, this is a reconfigured app for Mac.
The reason why compilation is necessary is the difference in CPU platform. iPhone and iPad adopt "ARM", Mac adopt "Intel(x86_64)", and the instruction set (machine language/ISA) that the CPU can directly understand is different. Even if an iPad app is run on a Mac, the developer must generate an app consisting of the x86_64 instruction set based on the source code.
But next-gen Macs are different. The "Apple Silicon" CPU (SoC) uses the ARM platform and operates on the same instruction set as the iPhone and iPad. There is room to run the iPhone/iPad apps distributed on the App Store without recompiling from the source code. In fact, the WWDC 2020 keynote featured a demo of running iOS apps on a next-generation Mac.
Although the actual product has not been released and detailed information such as operating conditions has not been revealed, it is certain that the next-generation Mac will be closer to the iPhone/iPad. If system software becomes standardized in the future, the compatibility of apps will increase.