Eh not necessary. For example does code in QT compile to Android (NITDroid)? Even in Ubuntu there aren't QT libraries included by default (at least if I ever install a QT program I have to also install all the QT libraries associated with it).
Wikipedia says that there is an experimental support.
# Android-Lighthouse – Experimental development of Qt for Android.[30]
About libs, you install it once and forget about it. So, I see no problem.