I can only speak for myself (and by extension from my own group and experiences), but I will have to sound off in the negative here.
I strongly advise you don't; at least not in this fashion. It sounds like you're trying to short-cut doing any kind of map, and that will lead to inherently a worse experience. I believe theatre of the mind is more problematic to run because you have to keep everything spacially in mind for at least yourself (I have, in 33 years of DMing attempted it only extremely rarely, and for throw-away combat I just really couldn't be bothered about.) It's not like scribble map on a sheet of paper is much effort, even if you don't want to use actual figures. Even in a normal RPG, to do theatre of the mind combat requires the DM to be described everything, the terrain, the PCs, what they are doing. You can sort of get away with some sort of abstraction in something like a chase, but then, you're only worrying about relatively distances, and it's easier to do so because you're only concerned about opening and closing that distance - chases are, of course, very linear by nature. Indeed, most of chase rules I've seen work largely in this fashion. But they ONLY work for chases.
Your system isn't even trying here, I'll be honest; you've abstracted away movement - which you wouldn't even do in a normal RPG, whther you use a map or not. By removing any kind of maneouvering, you remove a critical (nay even, the single most important element of combat). You will get the Paradom Grand Stratagy Combat Problem as well, that for all the complexity, it boils down to just "two blobs rolling dice at each other until something dies" or, at best"two blobs of units moving slowly towards each other. You have also directly taken away any kind of agency from the PCs, because you've abstracted it down to just opposed rolls (combat is just now RNG). There's no real decision making to be made here, no tactics. (Heck, you haven't even considered what happens when multiple mechs engage the same target, I think.) No, the minor decision and range or what to shoot does not constitute enough worthwhile input.
I'll be brutally honest - the system as written comes across like you don't really WANT to run BattleMech combat and are trying to make a load of shortcuts so you have to do as little as possible. That may not be your intention, but that is what your mechanics as they stand say to me. As they are written, they definitely won't be fun, except for the people that just like rolling dice for the sake of rollng dice. Let me put it this way. Would you resolve ALL of your roleplaying combats in this exact fashion? Because if you wouldn't, then, like, don't try it with mech combat, just run it in the same way. You don't need figures or a mapsheet or terrain for running RPG combat, after all, you can do it on a scribble map on a pirce of paper and a pencil if you have to. (Replace paper with "scribble in Paint" or something if doing it online.) But bare minmium, you, as DM, DO have to know where things are relatively to each other even if you are only describing them to the players and don't show them a map of any kind, because that's your one job. These rules are not doing that - you're trying to make rolling dice the combat dungeon master.
This is not hypothetical on my part: I have tried, very briefly, a combat system like that for wargaming aerospace in support of the ground game. It developed into just throwing dice at each other was was extremely boring; we abandoned it immediately. Like "halfway through the forst game I tried it" it was that boring. I have experimented with other such systems for stuff like parties of fighter pilots (notably both of these are aerospace, which obviate the most critical factor in ground combat - the terrain) and in the end, found them not even remotely a substitute for getting the figures out and doing it "properly."
Again, I can't speak for anyone else, but as a player. personally, I would not want to play with these rules.
