The answer depends on why you have a diode separated power supply to begin with. You may not be achieving your original goal by tying the pins together if what you're going for isolation.
That said, in most cases a few microseconds of bad behavior on input pins of digital ICs is usually OK, in that the IC may survive it, but you may have some bad behavior when things are not within the specifications. You need to see if this bad behavior is OK for your application. It may involve, for instance, your LEDs turning on for a brief time when they aren't supposed to. If this also leads to a high current inrush through the digital inputs of your MAX, that could be a bad thing. There could be IC damage and set your uC in a reset loop if it's power supply in unable to sustain whatever the badly behaving MAX7219 demands.
This bad behavior can stay on as long and the power supplies put either device in a region where operation is not specified. The longer it keeps up, the more likely you are to cause actual damage. Its never a good idea to power things through digital lines, and that is precisely what can happen in this condition. i would recommend using a level translating buffer such as the SN74LVC1T45 and others of its family to do a better job dealing with connections across power supplies that aren't guaranteed to exist together. You simply put a resistor between the Vcc ad ground on both sides, something in the 10-100K range, and when one side loses power, the buffer shuts down and the line is effectively disconnected.