Mobile Phone Emulator

Does Unity offer something like an mobile device emulator like other IDE’s where I can test a game out on Android and Apple devices so that I won’t have to actually build and deploy on an actual physical device? This would save a tremendous amount of time.

Not integrated into the editor itself, but you can of course compile your game as normal for the target platform and run it in any emulator you want. Or you can use Unity Remote, which allows you to preview the Game window on a device and test touch/gyro/accelerometer input etc without compiling.
https://docs.unity3d.com/Manual/UnityRemote4.html

Yes, exactly. Just hit play, I mean what is the problem with that? Well, if you need touch input, download unity remote app from play store to your phone, connect it through USB and follow the instructions.