No – as long as it matches the output impedance of the amplifier that
it’s plugged into. In a valve amplifier the output transformer’s
windings match the speaker to the power valves. So the amp will sound
the same if you use a 4-ohm speaker plugged into the 4-ohm output, or a
8-ohm speaker cabinet plugged into the 8-ohm output, etc.
There are a few postings around the Internet that claim it’s always best
to use all of an output transformer’s secondary winding, which usually
translates into using the 16-ohm output with a 16-ohm speaker. Assuming
the output transformer has been correctly built, there’s no reason why
there would be a significant difference. And no matter how many times
I’ve experimented with this, I can find no tonal difference.
For myself, I tend to choose 16-ohm speakers purely for consistency, and
it makes it easy to mix speakers within a larger cabinet if all of them
are the same impedance.