Given that Wikipedia says UNIVAC was discontinued in 1986 I’m pretty sure the answer is no and no!
Its OS, OS 2200, does have a C compiler. Not sure if there ever was a C++ compiler, if there once was it is no longer around. But that C compiler is not being kept up to date with the latest standards, it only officially supports C89/C90 - this is a deeply legacy system, most application software is written in COBOL and the OS itself itself is mainly written in assembler and a proprietary Pascal-like language called “PLUS”. They might add some features from newer standards if particularly valuable, but formal compliance with C99/C11/C17/C23/etc is not a goal.
The OS does contain components written in C++, most notably the HotSpot JVM. However, from what I understand, the JVM actually runs in x86-64 Linux processes on the host system, outside of the emulated mainframe environment, but the mainframe emulator is integrated with those Linux processes so they can access mainframe files/data/apps.