Does using an uncoated or coated Pantone swatch in software actually matter?

Pantone swatches for uncoated stock are the exact same colours used in the swatches for coated stock. The only difference is the swatch books show what the colours look like when printed on different stocks.

There is a real difference in how these colours will look depending on what stock they are printed on. Colours on coated stock are generally richer and more vibrant, than on uncoated stock.

This should give you some idea of how different they look:

It doesn’t matter so much in software, as long as you, or your customer knows what the colour will look like if printed on a different stock, and as long as your printer knows which swatch book he should be matching the colour to.

For example, if you set an uncoated colour, and print it on coated stock, and the printer uses the wrong swatch book for colour matching, then it’s hardly the printer’s fault if you messed up. OK, so he might notice the mistake, or he might not (who knows!). So with that in mind, it’s probably best to choose from either the coated or uncoated swatches in the software, as per the stock you intend to print it on. Don’t leave things to chance.

Oh, and to answer your last question, they won’t look any different in colour managed software, unless you enable the the print preview and change the profile setting from coated to uncoated stock or vice versa - but that will affect the whole document, so within the same document both colours will look identical.
This example from Illustrator with colour previewing enabled.