Can fallback WiFi be used for anything without captive portal?
Yes, I use fallback AP everywhere and captive portal nowhere 
What services are available on the fallback AP without captive portal?
That always depends. ESPHome only compiles features that you actively add to your device config (yaml) 
If you search for a particular function (ota, web server, etc.) maybe just tell us so people can help you what are you looking for 
Describe the goal, not the problem
It’s all too easy to fall into the trap of the XY problem . If you describe your goal first, then others can understand what you’re trying to achieve.
I am searching for which services ESPHome offers when Fallback AP is active and no captive portal is enabled.
Remember that WiFi is in AP mode then and not in Station mode.
That is my problem.
All esphome components I commonly use do work perfectly fine in AP mode. But as written in my previous post
Crystal balls 
are rare this time of the year 
If you want the components in question to stay secret you might just check them yourself 