They actually did attempt that mission ITTL. Unfortunately, even if you had flown such a mission the odds of success were extremely low. The Russians are known to have a close to 100% failure rate on it's Mars probes.
If you look at one of the earlier posts it mentions the Mars Sample Return mission, it was a fully successful launch. But the hardware failed after TMI, as had happened on countless other missions IOTL. The Russians just weren't very good at the exploration of Mars. But they basically dominated the exploration of Venus.
Soviet failures to successfully reach Mars with a functional mission package are an infamous fact of OTL, whereas they have been more successful with probing Venus.
But ITTL you've asked us to believe they could make N-1 work, on a timeframe that actually beats Apollo to the Moon. And you've made a believer of me. To explain this, I've been assuming they are doing something different to be more successful--specifically devoting more consistent and disciplined effort toward making more reliable hardware.
It's hard to see just what objective facts about missions to Mars versus Venus should make the latter attainable for a relatively crude state of the art but not the former. It is true that Mars is farther away; furthermore because Venus is closer in toward the Sun and Mars farther out, transit times to the former are quicker--meaning, less time for things to go wrong. But I don't think the time frames are so far out of proportion that that's a sensible explanation all by itself, that Soviet hardware could survive reliably for one transit time and not the other, with any large difference in survival rates. The rigors of one launch are about the same as the other.
So it seems to me that Soviet failures vis Mars are a run of bad luck, and in an ATL where they could make missions such as their N-1 based lunar missions come off without a fatal hitch, they could make better space probes--some would be bound to get through to Mars I'd think.
Especially because, while the N-1 is not quite a match for the Saturn V, OTL we never used the Saturn V (or even 1B) for launching space probes, just Apollo mission hardware and Skylab. If JPL or Ames could have had a contract to make a Mars or Jupiter or Saturn probe to be launched from a Saturn V--well, that would have been a sight to see!
So if the Soviets do make an interplanetary probe launched from an N-1, it will far outmass any probe with a comparable mission ever launched OTL. Sheer mass is no guarantee of success-it might just be a more colossal failure.
But it gives margin for robust structures and for redundancy, and those ought to improve the odds of at least partial success.
I suppose, if one power uses its biggest launcher to launch a mega-probe, the other will be pretty likely (well, far more likely than otherwise anyway) to match it with one from theirs. So an N-1 launched Mars probe might lead directly to an American probe lofted by a Saturn V upgrade, a mighty piece of technology indeed!
You've got the same dilemma here you have with envisioning the outcomes of orbital science in the space stations of course--you've got some margin to just recap what OTL space science has discovered, in a scrambled order perhaps. But at some point we have to imagine that a deep space probe or an orbital experiment will turn up something OTL has yet to discover--but what? Whatever we imagine will probably look silly and unsubtle compared to what real space science, when God willing we ever actually get around to it
, has in store.
I don't think the Russians will suffer the same curse on Mars missions they did OTL, or anyway even if their success rate is somewhat less than American, it will be better than OTL--and both powers might be attempting more missions, on a grander scale, so that there will be Soviet successes to eclipse the failures rather than the unbroken record of frustration OTL. Objectively I suppose the longer transit time does put more of a toll on the quality of the probe design, but Soviets should be closer to US standards here.
Unless we suppose some hidden variable--such as the Great Galactic Ghoul--that upsets everyone's calculations (American missions have not enjoyed perfect luck either) and favors the Americans (we have nevertheless had pretty good success after all). OTL the discrepancy between Soviet and US quality control levels might explain it, and might not. If some of what has happened to the Russian missions is just random bad luck, then this timeline is a new roll of the dice.