It's possible to run B4A in REAL Linux. Using VirtualBox (or any other emulator), it's possible to run it in virtually any device... but in Windows running into an emulator.
To run it in REAL Linux, it's necessary to use Mono. B4A is developed in .net 2.0, which is supported in Mono. If the IDE don't use pinvoke it's possible to run it. If not, it's possible to adapt it to run Linux or MacOS under Mono.
(Sorry for my very bad english)