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.
No, you cannot do what you are thinking (if you are thinking what I think you are thinking) with just any SPI devices.
The devices you have pointed to are not SPI devices, but shift registers. They do not operate in quite the same way as SPI, however SPI can be used to drive them.
They are actually more akin to JTAG than SPI.
In a shift register or JTAG device the data input (TDI in JTAG parlance) is fed into a simple shift register, and the final bit output of the shift register falls out into the data output (TDO in JTAG). That's not how SPI works.
In SPI the SDI and SDO pins are completely separate and the relationship between the data in one and the data in the other is purely down to the whims of the chip. It is common to clock in a command or register location into the SDI pin and, on the next byte, the contents of that register is clocked out of the SDO pin.
So no, the input doesn't "fall over" into the output like a shift register.
If you want to reduce the number of CS pins used then you could use, say, a 74HC154 4-to-16 decoder to connect 15 devices to just 4 CS pins (reserve 1 pin for "no device selected").
If all your devices are shift registers, or operate like shift registers, and not real (register based) SPI devices, then you may be able to cascade them if they all work in the same way. That, of course, is not guaranteed unless they are all the same device.
Best Answer
First off if there is any opportunity to eliminate the USB-to-RS232 cable then do so. This would also allow you to get rid of the MAX232 as well. Instead use an FTDI type USB-to-TTL_Serial cable. You can get these for 5V targets as the TTL-232-5V cable or for 3.3V targets as the TTL-232R-3V3 from http://www.mouser.com. It only takes a simple 1x6 header to connect to your target.
One term used to describe power getting into rails from inputs that are attached to a powered device is "leakage". Unintentional current feeding into powered down electronics through input protection diodes.
Leakage of the type being described can indeed be problematic. The negative bias you are seeing is particularly disturbing. Here are some things that can result from this...
The best solution for input leakage problems is to isolate the powered inputs from your circuit so that in the powered down situation there are no current paths. This can take several forms including the use of open collector or open drain buffers with pull-up resistors to the powered down side of the circuit. There are also buffer ICs that can be used (look at parts in the 74CBTLVxxx family).
Sometimes a easy out fix for leakage is to put a resistor to GND on the affected voltage rail. This can shunt the current from the input protection diodes to GND and keep the voltage level low enough that it reduces chance for latchup in the affected chips.
In your case putting a diode in the voltage rail of the MAX232 may not be the best idea. This would reduce the operating VCC of a chip that wants to have a healthy rail - particularly because it wants to voltage double and voltage invert that rail. It would be far better to identify the signal lines from the powered up PC that are sitting at a negative level and find a way to prevent them from sinking current out of the MAX232 chip.
You may want to consider looking at some of the newer RS232 level translator chips. There may very well be some that are specifically designed to prevent the problem that you are seeing. Such chip may be TI's MAX3223. When I've used that I never noticed leakage problems into the circuit from a live RS232 connection - but then again I have not specifically characterized its operation either.