After days of reading tech docs, MECP books, other posts, manuals, and my own tests, I've came up with a somewhat more detailed answer to my question.
I'm still no expert but my belief is there is no way to "fry" the amps unless the outputs are either short-circuited together or subject to very low impedance. Therefore in the previous diagram or similar situations, the amps should be fine as long as a suitable sub is hooked up to the circuit.
However, there is potential for damaging subs; especially if both amps are not set exactly the same. This would be due to either extreme excursion, clipping, overheated voice coils etc....
I came to my conclusions by first understanding the principles of bridging in 2-4ch amps and how mono amps work in relation to those.
In a bridgeable amp, for each channel only one terminal has a signal while the other references ground. The second channel is inverted but on an opposite polarity thus giving an identical output. When both channels are bridged you get double the output.
"Strappable" mono amps use this same principal because the positive terminal drives the signal while the negative is a ground reference (like a single channel in a 2ch amp). The second amp will have a switch that will allow you to invert the positive signal and use it as a negative, thus doubling your output if you use both amps together.
The Alpine M350 in my example (like many other Class D amps) don't work on this principle. In essence it's already internally "bridged" because both the positive and negative have a signal (regular & inverted).
"Bridging" two of these as the diagram showed would not have any positive effect on audio output but possible a negative effect if both amps weren’t in sync. If anything it would be a neutral effect; like cutting two apples in half and putting two halves together, you get one apple and a waste of time.
Yes you can bridge two mono amps, only if they were designed to do so, otherwise it's pointless and potentially dangerous to the subs.
So that's the long answer to my question with a why and a how.
Thanks for all the previous responses from you guys. Someone please correct me if I’m wrong about anything I've said.