Generally speaking, most air horn compressors draw more current than the stock horn so it is a good idea to fit a relay even though it works without one. Some compact air horns meant for motorcycles would be fine without a relay, and more than loud enough.
Most common air horns (Hella, “Maserati”, etc) take a wee bit of time to spool up. I use a much larger compressor from a Citroen DS. The horns come instantly on and are much louder.