Does adding silence to a flac with an ffmpeg filter result in any quality loss?

I'm attempting to add a few seconds of silence to the end of several flac audio files. One recommended method is:

# ffmpeg -f lavfi -i anullsrc=channel_layout=stereo:sample_rate=48000 -t 5 silence.flac 
# ffmpeg -i 'concat:input.flac|silence.flac' -c:a copy output.flac

When I do this, however, the output.flac appears to have the same length as input.flac (as reported, e.g., by ffprobe, mediainfo, or when played in vlc). I'm not sure why it's not working, but the following also does what I want by extending the file by five seconds as silence:

# ffmpeg -i input.flac -af apad=pad_dur=5s output.flac

I've read that the latter approach has the disadvantage of re-encoding the file. But if the input and output are both flac, does that mean the re-encoding is done with no quality loss? Separately, any suggestions on why the first method is not generating a longer audio file with five seconds of silence at the end?