If you have a switch/button hooked between digital pin 13 and ground without a resistor, and if the AVR is trying to drive that pin high, as it would to light the onboard LED, and the switch/button is thrown/pushed to create the connection to ground, the LED will not light and it is very likely that you will damage the AVR.
This isn't something you want to test.
that is something that i personally have tested several times a day for last 15 years and no smoke yet. just as predicted by ohms law and most atmel specs.
arduino creators have been criticized for poor design decisions and hooking an led to gnd might be one example. those experienced and knowledgeable in hardware probably need nothing more to be said (but as usual i will anyway, lol).
there are several reasons for connecting led to vcc instead of gnd. biggest one, besides proper led wiring protocol, is you can share a button. this is why the first thing i do on all "official" arduino board designs (uno, promini, nano, etc) is rewire to vcc so that the universe will be in harmony.
ive done it so many times it only takes a few seconds and of course costs nothing in additional components.
thankfully most other boards like usbasp and atmel tools are designed correctly.