We know microgravity is terrible for us but we don't have data on 1/3 gravity. We might be fine. Or maybe we'd be fine if we took this drug, did some weight training, and added twenty minutes of centrifuge every day.
For the trip, there are several ways we could set up spin gravity.
For more on this "we don't really have the data for anything" problem, a humorously approachable read is "A City On Mars" [0]. Also the "nobody knows how laws would work" and other interesting complications.
I just wanted to say, I really appreciate your tangent here. Space travel didn't come to my mind at all and your comment made me feel the tiny things contributing to larger stories, for a moment. Caught me weirdly off-guard.
Bone density loss in space is estimated at a loss of 1-2% of total bone density per month of microgravity exposure. The worst cases of terrestrial bone loss are around 5% of total bone mineral density per year.
In many ways it doesn't cancel out. On Mars, things weigh less but their mass is the same. So, for example, if you are walking on Mars at a normal Earth walking speed, and you bump your shin on something, the inertia of your leg as it hits the obstacle is just as great as the inertia of your leg on Earth. In general, a lot of the little physical interactions that you rely on bone strength to get through scale according to mass / inertia (and muscle strength), not weight.
You're ignoring the prime reason humans aren't going to travel to Mars anytime soon: radiation. Good luck getting there without accumulating a huge dose of hard radiation that gives you cancer. This is why we should be worrying about building human settlements on the Moon first: we can put them underground (for radiation shielding, plus other benefits like avoiding meteorites), and the travel time is so short that the cumulative radiation exposure is very low. 3 days of exposure to cosmic rays is very low compared to a year or so, or at best 6 months.
Once we have manufacturing capability on the Moon, we can build much larger ships that have some decent radiation shielding.
Of course, the low gravity causes a bunch more problems. But here again, with significant space- and Moon-based industry, we could build much larger ships with spin gravity. This doesn't help the people working on the Moon though, but at least here we could cycle them on and off the Moon every 6 months or so, since the trip is only 3 days, so they could come back to Earth and re-acclimate to 1g periodically.
Among the dozen other serious health problems with zero/low gravity like oh serious eye problems, humans sadly aren't going to Mars anytime soon.
Then again this would need to be tested on the moon or in orbit first, might not make a difference even with the hormone.
(vitamin K2 might help too)