> Would there be any downside in using a telescope with a 2-inch diagonal, which adapts into a 1.25-inch eyepiece holder to do visual observing with 1.25" eyepieces, compared to if everything was 1.25" from the start?
Not unless the connection is of poor quality. If everything works as it's designed it won't be a problem.
> How would I go about actually attaching a planetary camera to a scope with a 2" visual back? For example, the ASI224MC has a 1.25" T-ring included.
I think you have two options, but I don't own an ASI224 I own an ASI120. So take this with a grain of salt. They probably connect the same though, just confirm it before buying.
1) Connect the 1.25 t-adapter to your ASI, slot it into a 2" to 1.25" converter and then slot the converter into your scope.
2) The ASI has an M42 thread that the 1.25 t-adapter screws into. Instead of screwing the 1.25 t-adapter in, screw in an M42 to 2" adapter.
I think optically both of these options would work just as well.
> but I assume this isn't an ideal setup since it adds an additional optical element in the form of the diagonal mirror.
You don't need to put a diagonal in to make the 1.25 to 2 inch converter work.