Can I add the superuser binary without a custom recovery? Is there a way to force the binary install through terminal or PC or app?
Generally no, but it depends on your device. For example, if you have an older non-updated Amazon device, you can usually root it with as little as an app install. For devices that haven't been exploited yet, however, there's little hope besides asking the community on xda and such very very nicely. It's a good idea to look for "bootloader unlockable" devices when you're looking to purchase a new Android device, to show the corporations that people want this.