Not unless you make it open source and require your users to download and compile it to their device with Xcode on their own. Not going to work for most, and without a developer account, they'd have to redeploy to their device every week, since that's how long the license lasts.
yes, you can i heard instacart for example uses their enterprise cert signed app for their drivers/deliverers. Drivers are instructed to go into settings and change things to allow loading that app
I wouldn't call that an alternative to the App Store, as that's exactly what the enterprise certs are for - internal distribution to employees (or more likely in this case to be contractors but whatever). Getting regular users to go in to settings and change things just to install your app is not feasible.