I have some experience studying two languages together, though my situation is pretty different from your own. Basically, after I had been learning Japanese on my own for about a year (while doing my BA), I got a job in China, so I kind of put Japanese on the side-burner for a while and did a summer intensive in Chinese that was the equivalent of an academic year of the language in nine weeks, and immediately after that left for China. It wasn’t until I had been in China for a little while and felt more comfortable with Chinese that I started focusing on Japanese again, and I’ve kept up study of both ever since, and I think my knowledge of Chinese has really sped up my Japanese learning. For starters, I would guess in any Chinese class you take the approach to studying characters will be much different from most textbooks’ approach kanji, so you end up learning Chinese characters at a much faster rate than you would Kanji (for one, there are just more to learn), which then helps you a lot later down the road with Kanji, since many of them are the same or similar (especially if you’re learning traditional Chinese characters, though even simplified will have have a lot in common). Additionally, there’s a lot of vocab overlap (even though it sounds different, being built out of the same characters and sounding kinda similar helps a lot).
For me, balancing both of them when I’m not studying in a classroom is a little tricky sometimes, but if you’re in a program learning both, that should help you pace yourself and balance the two appropriately. As for after graduation, one my one of my majors in college was French, and it actually hasn’t been too hard to maintain that along with the other languages I’m studying because my French was advanced enough by the time I graduated that the kind of activities I do (reading novels, watching movies, talking to French people) to maintain it doesn’t really feel like the same kind of thing as grammar and vocab memorization, so I have energy for both, though I admit all the things together take up a big proportion of my not-work time. I think once you get to an advanced level, improvement gets a lot slower, but maintaining your level gets a little easier, so I imagine you could manage it.
That sounds like a really cool program, by the way.