Well, I take issue with the statement "like most games"; as if continuous time were the natural default choice in ludological circles; and turn-base some form of exception that requires distinction. :>
Everyone is welcome to explore the boundaries of roguelikes, so the answer is going to be "yes" regardless of what the question is. The spirit requests that you, yourself, are in the spirit of "roguelike", and you are the only one that knows if that is true. (It is like Nanowrimo, when someone asks if they can submit 50,000 words of "a". Yes, you can. But why?)
As for the issue if discrete time is a requirement for roguelikes? I personally do not believe so. I think, however, it is a natural consequence of roguelikes. Anytime you start to build a tactically focused game, you naturally move to discretization of space and time. (And of health, esp when taken to the 1hp extreme)
Chess isn't played by turn on a grid because of limitations of a ASCII terminal or lack of continuous input modality. (My most interesting example of chess is that within Ultima Online. Chess there was implemented as merely tokens and graphics of a board. The two players, like with the real world chess, can place pieces where they desire, and at any time, with no space discretization or time discretization present. But naturally, just like a real-world chess (which plays in a continuous space) one would play it in a discrete manner to enjoy the game.)
One interesting game to look at if you are thinking of continuous time is https://en.wikipedia.org/wiki/Dungeon_Master_(video_game) . This is a discrete spatial game with a continuous time model. From a modern perspective one could argue that it is ... broken .. because of it, but it is a very interesting example that we rarely look at. (Note this is different from time-expiry turn based, like the old Ultimas, or global wall-clock limits, like Jacob's Matrix, as those will alter the world heartbeat to the turns)