Does enabling sideloading allow applications to be installed or run on the device without consent? I'm concerned that enabling sideloading of applications may allow malware to be installed.  However, I'm aware that Android gives a "Do you want to install this application?" dialog while installing an APK, intended to prevent unauthorized software installations.  I'm wondering if a workaround exists that can defeat this security measure.

Barring unintended behavior such as security vulnerabilities, does enabling sideloading make it possible to install or run applications of any kind on the device without consent?
No. Installing packages is still a privilege reserved to the package manager, which is a system app (i.e. it's inside the ROM), and the package manager doesn't offer an interface to avoid the confirmation dialog. This is by design.

That said, if USB debugging is enabled (in the developer options), you can use adb to install an APK file from a PC, with no user interaction. This possibility exists regardless of whether installing apps from "unknown sources" is enabled. USB debugging is a so-called secure option: only system apps can change it.