I was wondering, is it possible to play guitar, improvise, with delay to a piece where no musician plays to a metronome. Not the drummer, not anyone else.
How can the guitarist know what to set the tempo to, or what delay length to choose?
Imagine if instead of having a delay effect on, you just played every note or chord twice with the same gap between each repeat. Then it's just a matter of other musicians playing along with the tempo and rhythm that you set for your repeating notes.
As long as the other musicians can hear the guitar and the delay effect well enough, you can all play along using the delay effect itself to set the rhythm as a kind of metronome.
Note that if the guitar player doesn't have a good enough sense of rhythm and plays too many notes off-time, they can trainwreck the whole thing, since following the guitar rhythm is what makes this type of playing work. So the guitarist takes on the role of rhythm master from whoever else normally is in charge (usually the drummer, but not always).
That's why having a control pedal to use as a tap tempo is great.
But I have found that a dotted 8th at 120BPM works for me with many different tempos to just help me fill empty space in the song. That's my default delay setting. As long as you aren't playing staccato type things it works well.