That question would require writing textbooks but I try a short one.
In electrically-powered systems (PSUs - PCs) the sinusoidal wave deviates from its normal form whenever there is a sudden change in the system such as by addition or removal of loads or power outages. This short (miliseconds) sudden deviation/change from the normal sine wave is called transient.
They can have external srouces like a power outage. Also interal sources. Every time you turn on, turn off, load, or unload an inductive device, you produce a transient. Power switching, FETs in other components in the system (motherboard, graphcis card) also cause transients.
Also when an electric circuit is switched on, the current reaches to maximum value almost in zero time and when the circuit is switched off, the current drops to zero from maximum value in no time.
But if there is inductors or capacitors in a circuit (which are in PSUs), the current will not become maximum from zero or from maximum to zero in no time. The current will take a finite time or one can say it is a gradual process. Thus the electric current which takes finite time to become maximum from zero or zero from maximum in circuits having inductors and capacitors, then such currents are called transient currents (in that certain finite period of time).
Transients, depending on conditions, result in voltage drops. However, in a good quality the voltages should remain within the regulation limits defined by the ATX specification.
MOBO and CPU being "healthier" has many factors. One of them is VRM (voltage regulation modules) of the board itelfs and how it handles the power it gets from PSU and how it distributes it to CPU, RAM, PCIE slots and all other components, which is a complicated process.
That 350W doesn't remain 350W constantly. If this is the maximum some components will need/draw it will change in different stages of the system's operation depending on the load. This is more a matter of efficiency than remaining healthy and also efficiency ratings. A PSU rated at 550W would be usually more efficient providing a 350W load than a 50W load. It's own health and whether it would keep other components healthy are a result of design and build qauality and how tight its regulation and how good its protection mechanisms are.
In real world scenarios, a PSU is working with changing loads all the time, depending on how busy the CPU or graphics cards are. So it is very important, for the PSU, to be able to keep rails within the ranges, defined by the ATX spec. The smaller the rail deviations from nominal voltages the more steady the system will be and as a result less stress will be applied to the components.
P.S. Didn't really read it again to see if any part needs changes. Hopefully, others will have some input too.