Here's a great topic about geoprocessing tools and spatial reference (coordinate system) that hopefully will answer your question.
Tools that output a new feature class from multiple inputs with different coordinate systems have logic to determine the coordinate system of the output. If the inputs have different coordinate systems, coordinates of one (or more) of the inputs have to be transformed during tool execution (leading to increased processing times). Sometimes, these transformations can really affect results, especially for large areas with features with sparsely-spaced vertices - think of a two-point line covering a large distance, as illustrated in the linked topic
(This is why the Densify tool exists)
Knowing this logic and the effect coordinate system transformation on processing and output is important stuff and quite overlooked.
For your data, it seems the coordinate system of your datasets would be similar enough that they wouldn't have a big effect on area/length calculations(?), but maybe so if the extent of your inputs is large?
Hope this helps.