The specification does not require any delay between bytes. It says:
PRIORITY OF MIDI RECEIVING
An instrument capable of receiving and processing incoming MIDI data must give priority to its MIDI In port over its local functions such as the front panel or keyboard. It is critical that incoming data never be ignored or mishandled due to the processor's attention being elsewhere.
At 31.25 Kbaud, one byte is sent every 320 microseconds, which means that proper handling of the received data during any long-term or ongoing MIDI communication will require a high speed microprocessor.