You can try steeping coffee grounds in tea bags and it can be done, however, the results aren’t very ideal which is why other methods of brewing coffee exist in the first place.  This is true for the reverse, you could finely ground up the tea leaves and put them through a drip coffee machine but the end results won’t be ideal either.

What will happen if I try?

When coffee is ground up coarse or fine, it is brittle so it breaks up into larger and smaller size particles.  Depending on the size of the small holes of the mesh tea bag, there is a good chance some of the finer particles will seep out.  

This will cause the coffee to get muddy at the bottom with residue, much like a french press.  In itself, this may not totally bother you, but for some, it may.

Why wouldn’t it taste as good?

Coffee grounds dry up and go stale much quicker than tea, so it wouldn’t make sense to leave small coffee bags out for any real period of time.  The rich oils that get exposed from grounding add so much flavor to your final cup.

However, if you placed your freshly ground coffee right into a tea bag and immediately steeped it for 4 minutes, it would taste quite nice.  The main reason it is said that it won’t taste good is that you wouldn’t just do one serving at a time like that (because then you’d use the other coffee methods like french press or pour over), you would make a bunch of bags at once.  Which would mean that last bag wouldn’t be as tasty.

With tea it has the opposite effect, ideally, you don’t want to crush the dried leaves and leave them whole as much as possible as the oils stay intact.  Tea needs to be steeped in the water for it to reach its true potential which is why it wouldn’t work in a drip coffee machine (but does work well in a French Press).

You should try it for yourself, what’s the ideal situation?

Trying it out isn’t a bad idea and I would encourage you to try it in situations like not having access to a coffee shop or coffee machine and would like something different than instant.

An example of this would be if you are going camping or a trip and need to pack light.  If you are not taking anything special for coffee production or have access to a place that offers coffee and just have the ability to boil water, then putting some of your favorite coarse grinds in a tea bag might be a good change from instant coffee.

You wouldn’t want to do it long term since the grounds will easily dry up and lose its rich oily flavor.  It would help if you kept them in a plastic ziplock type bag to maintain freshness, especially if you are using your favorite grounds.If you would like to try it, you could try buying empty tea bags to use with your own ground beans or Folgers has a product called “Coffee Singles” which is exactly this, coffee in a tea bag which you steep.  Each bag is plastic sealed to help with freshness, although less great for the environment due to more packaging, however, for seldom use for a specific situation it could be worth it.