Was there a time when Linux did not separate User and Kernel space?
That depends on how you define the terms "Linux", "user space", and "kernel space".
Remember how Linus Torvalds originally created Linux. Linus saved some money to buy himself an (at the time state-of-the-art) PC with an Intel 80386 CPU. He wanted to understand how the 80386 works, and he thought the best way to do that would be to write some low-level hardware code in 80386 assembly. At the same time, he was also dissatisfied with the performance of the terminal emulator running under Minix he was using to log into the university.
So, he decided to write a terminal emulator in 80386 assembly which you could boot directly. For this, he needed to write a bootloader, a keyboard driver, a (character) display driver, a serial driver, and a driver for whatever protocol he used to connect to the university.
Soon, he found that he also wanted to download files from the university, so he had to implement some file transfer protocol (probably ZMODEM, but maybe he chose XMODEM for simplicity) and also a hard disk driver, partition table parser, and a filesystem driver for the Minix filesystem. Because he also wanted to continue working while the terminal emulator was performing some long-running operation (such as a file download), he implemented multithreading.
This is the point where he realized that he had already implemented some significant portions of an Operating System, and so he thought it would be another fun project to turn the terminal emulator into one.
At some point after that, he accidentally mistyped a command and overwrote his Minix partition with a backup. Now he had a choice to make: reinstall Minix or finish his Operating System and use that instead.
When he came to a point where his Operating System was capable of running simple programs, he decided to upload it to the university's FTP server, and named it Freax (he thought that naming something after himself was pretentious and arrogant). The sysadmin of the FTP server didn't like the name, though, and decided to rename the file to Linux, which he thought sounded better.
Another while later, Linus made the very first public mention of Linux in his famous message where he stated that Linux was so tied to the 80386 that it would never be portable to anything else and where he predicted that Linux would never be big and professional.
Now, the question is: at which point in this journey did "Linux" become "Linux" and at which point in this journey did Linux become a "kernel" so that talking about separation of user and kernel space even makes sense?
As I said at the beginning: it really depends on how you define those terms.
In other words, was there a time when my rogue program could have caused similar havoc to a Linux system?
There was certainly a time in its evolution where the piece of software which later became an OS and which was later called "Linux" had no protection, had complex enough services that you might get away with calling it a "kernel" and had independent enough subsystems that you might get away with calling those subsystems "programs". For example, in a "real" Unix system, the terminal emulator and the file transfer would typically be two separate programs and the thing that coordinates the two and which houses the code for accessing the serial port, the hard disk, the screen, the keyboard, and the filesystem would be the kernel.
But was this piece of software "Linux"? I will leave that to you to decide.