For actual coursework or professional job requirements, no, you don't need a fancy camera. If it helps you curate an interest in our urban fabric, buildings, details, or travel, then it will probably pay off in the long-term though that payoff might be intangible. 

I have a D5100 which is even older with 3 lenses and it's still a solid camera for DSLR work. I probably use it 2-3 times a year. I also have a Ricoh GR2 which I greatly prefer for 90% of situations, travel, arch photography, and it takes stunning model photos too. I use it every week. 

Agreed. A fancy camera is not needed here. No point in wasting precious dollars behind the thing that is not needed at all 

If it's no older than 10 years and has a good quantity of available lenses, then it's more than good enough for anything less than professional photo work.

If it's about learning how to see or observe, you don't need a camera for that. If it's about learning about the technical aspects of photography, then (mostly) any camera is fine. Is it a good deal? I don't know - Is it just the body? Does it include lenses? Check the web and see how much a second-hand D5200 goes for. Also, ask yourself how often you want to lug around a DSLR and for what purpose. 

This was my camera for undergrad and most of grad school.

Did a bit of amateur arch photography. 

$200 is probably o.k, I had something similar starting out but as I started bringing the camera around international travels or road trips I noticed I would use the phone camera a lot more (dslr's are heavy, especially if you have several lenses). For my 'hobby-level' photography these days, I'd prefer a smaller mirrorless. 

If you have a nice phone that's probably good enough, if you're looking to photograph studio sites or school models, more than likely your school or university will have a equipment lab that'll let you borrow a camera. 

But does it come with those fancy instagram or snapchat filters and lenses? 

Not that high quality filters. But also, not that low where you need to spend your hard earned dollars. The filters are present but you need to compromise with the quality to a very negiligible extent Mybpcreditcard

You're going to want high-quality images of your non-digital work for your portfolio. It makes a huge difference in how professional your work looks

Useful for school, but not necessary.  My school had cameras students could check out to take photos of their work for pinup or portfolio. I bought a starter Nikon DSLR when I was in school, and lugged it around Europe during my first study abroad/backpacking trip. I ditched it for the second European backpacking expedition. I've used it once professionally.  We needed some nicer photos, but the situation didn't merit hiring a professional photographer.  Mostly the photos we take are to capture work progress, so we normally take decent point and shoots that the office provides. They're small enough that they aren't a hazard when you need to climb scaffold or in a harness.