Hi,
Qt is not dependent on the kernel version so using the 3.14.52 kernel is not a limitation.
However, Qt5.7 might require some specific versions of some system packages. In other words, if Qt5.7 can be built on Ubuntu Trusty, yes it will work on our image with 3.14.52 kernel.
As a FYI, we are about to release Xenial with kernel 4.1.15 this week.
Regards,
Gary